I suggested in the comments above, earlier, that the Hindustan peninsula might have some appropriate examples. A cursory look at the Moghul, Maratha and Bengali armies, etc, did show that the cavalry forces put into field were of the order of tens of thousands of cavalrymen (Second Panipat, Tukaroi), I did not find an immediate example of a combined charge.

The Battle of Kars, 1745

However, I found a possible contender during the Ottoman-Persian conflict of 1743-1746. In 1745, Nader Shah was conducting forward defense of his borders, and met the Ottomans at the Battle of Kars, 1745. In this, Nader Shah is reputed to have won the day by organising a flank attack with 40,000 of his finest cavalry at the right moment.

I will describe the specifics of this account below, along with some sources.

Vatatzes' Account

From Michael Axworthy's 'The Sword of Persia' (location 5070):

The armies closed and engaged, but the cavalry of both sides held back. The infantry struggle went on for some time, each side attacking and counter-attacking; both commanders sending new reinforcements into the battle. One account says that, contrary to his usual practice, Nader in this campaign against the Ottomans had generally commanded the army from his throne within the camp, receiving word of developments and issuing commands to his troops by messengers. But by the early afternoon on this day his messengers were still telling him the fight was undecided, and he resolved to intervene personally. Nader put on his armour, mounted up and led a reserve of 40,000 Abdali cavalry in a furious attack against the Ottoman flank. Even then the fighting was still fierce, and two of Nader's horses were killed under him, but his presence encouraged the Persians to new efforts. Ottoman resistance finally began to crumble, and 15,000 irregular troops from the provinces of Asia Minor fled. The main Ottoman body retreated in confusion to the safety of the entrenchments around their camp. Nader followed them up, but withdrew with his men to his own encampments at sunset.

An accompanying footnote clarifies this is primarily based on the account of Basile Vatatzes, a Greek traveller and merchant in Persia. Axworthy describes Vatatzes' 'additional detail' on the course of the battle as:

Vatatzes, whose account (pp. 282-3) gives colour to what was previously known of this battle, is the source that says the cavalry of both sides were initially kept back. He says the Persian cavalry were superior and the Ottoman cavalry feared to attack them (one of the sources presented by Sha'bani also says the Ottomans did not have the will for a cavalry fight - Sha'bani 1977, pp. 34-7). By contrast, Ottoman sources suggest that their troops came close to beating the Persians (Cambridge History of Iran, Vol. 7, p. 309).

I should note that I did not access Vatatzes' account myself.

Quality of Vatatzes' Account

A separate article by Axworthy, 'Basile Vatatzes and His History of NĀDER ŠĀH' describes Vatatzes's work and its merits:

is patchy, often inaccurate, and his judgement is often suspect. ... Frequently, he reports the mood and general drift of events better than the details.

Nevertheless, the examples brought in the paper do not specify any numeric errors (although chronological errors are brought up), and Axworthy specifically says that Vatatzes' military descriptions are particularly useful on the count of their accuracy (e.g., on Persian titles) and thoroughness (e.g., on drilling the troops).

Astarabadi's Account

An alternative source is Mirza Mehdi Khan Astarabadi whose history of Nader Shah has been accessible in French since 1770 as Histoire de Nader Chah. This book contains the following description of the battle of Kars, much simpler and almost no (useful detail):

Le dix, dans l'après-midi, Mohammed Pacha s'avança avec cent mille hommes de cava lerie, & quarante mille d'infanterie, & campa au pied d'une montagne à deux parasanges de l'armée impériale, où, ayant dressé ses tentes, il commença de fortifier les endroits foibles, & de préparer ses canons & ses mortiers.

L'onzième, les deux armées étant rangees en ordre de bataille, le feu du combat com mença, à flamber, & ses étincelles atteignirent les étoiles. Après plusieurs successifs engagemens, l'armée Ottomane fut mise en déroute par l'interposuion de la' Providence.

La perte sut très-grande du côté des Turcs, leur genéral se retira dans ses retranchemens, & la nuit devenant obscure, les troupes conquérantes retournèrent à leur camp.

An approximate (though good enough in my opinion) (Google) translation reads:

On the tenth, in the afternoon, Mohammed Pasha advanced with a hundred thousand cavalry men, & forty thousand infantry, & encamped at the foot of a mountain with two parasanges of the imperial army, where, having erected his tents, he began to fortify the weak places, and to prepare his guns and his mortars.

The eleventh, the two armies being placed in order of battle, the fire of battle began to flame, and its sparks reached the stars. After several successive engagements, the Ottoman army was routed by the interposition of Providence.

The loss was very great on the side of the Turks, their general withdrew into his retrenchments, and at night becoming dark, the conquering troops returned to their camp.

Quality of Astarabadi's Account

The quality and level of detail is clearly without the colour that Vatatzes provided for Axworthy's account. Nevertheless, the quality of this writer is also in doubt (again by Axworthy, from "The Sword of Persia"):

The Jones translation contains many errors, particularly with dates and names, but is an accessible version for those who cannot read Persian... Mirza Mahdi was Nader's official historian, and understandably avoided including anything critical of Nader in his work. There are also indications that by the time the work was finished (about a decade after Nader's death), Mirza Mahdi needed to avoid offending some of the leading personalities of the Qajar tribe.

Nader Shah's Cavalry

I suppose to conclude, I should sum up what I noted on the Persian cavalry to support the argument that they could have done this (though, indeed, there are many cavalry units which could have done such a charge but did not).

Specifically, in another article on the Persian Army of Nader, Axworthy notes the particular quality of the Afghan (Abdali / Durrani) cavalry:

...his Afghan cavalry were probably the finest shock cavalry in the region.

Though the above article was illuminating in a general sense, and I'd probably recommend a read of it if the above topic sounds interesting, it doesn't bear much more discussion except to note that Nader Shah had plenty of troops armed and armoured exactly to fit the heavy shock trooper role as expected from a cavalry charge, and the troops most suitable are the ones that Vatatzes has placed into the role at Kars.

This is, regrettably, slightly circular as Axworthy's main source on the army is Vatatzes, of course, so this caveat should be borne in mind.

The numbers do, however, bear up for the general proportions of the army, with Axworthy quoting Jonas Hanway for 1744 (excluding some other larger tribes):

There were 13,000 guard cavalry, 20,000 cavalry from Nader’s own Afshar tribe, 50,000 Afghan cavalry, 12,000 jazayerchis and 40,000 ordinary musketeers. There were also 18,000 Turkmen, Uzbeks, and Baluchis, who served as light troops.

It should be noted that Nader Shah's son was conducting a separate campaign at the same time, winning a simultaneous battle near Mosul which completely destroyed the Turkish capacity for defense. Therefore, a good proportion of troops may have been with the son, making this charge unlikely, though Astarabadi implies that these were not troops from the main army (p 100):

Sur cet avis fa Majesté envoya le prince Nasralla Mirza pour s'opposer à ceux qui s'approchoient des frontières de Perse, & lui donna les légions victorieuses qui avoient été employées sur les confins de Karmanchah, du Loristan, & du Kiurdestan.

Same Google Translate option:

On this advice the Majesty sent Prince Nasralla Mirza to oppose those who approached the frontiers of Persia, and gave him the victorious legions which had been employed on the borders of Karmanchah, Loristan, & Kiurdestan.

Overall, on the balance of probabilities, I think that this here is a larger cavalry charge than at Vienna 1683, even if it does not stretch to the exact 40,000 as quoted by Axworthy, following from Vatatzes. Nevertheless, I think that if the numbers were ridiculous or the action improbable, Axworthy would have noted this much as he criticised Vatatzes for other reasons. Therefore, I would suggest that the largest cavalry charge we know of took place during the Battle of Kars.