How did Nazi Germany produce such an impressive portfolio of officers for WW2?

The correct answer was and is doctrine, if you look at german doctrine following ww1 and the revolutionary changes and forward thinking that they employed it's quite simple

I.e any one in the military who has read achtung panzer by Heinz Guderian will note how it's a basis for some currant doctrine

Hence later in the war the soviets caught up somewhat after there disastrous losses in the first years of the war

To understand fully the differences in command style and effectiveness, at least two other factors must be taken into account. These are to do with the history and culture of the armies involved -

1. The British and the French military system was developed over hundreds of years in large part to support their Empires. It was said of Bernard Montgomery that he was, "not one of us," and "not a nice chap." He wasn't a traditional 'Imperial Brit'. Many of the British commanders possessed a set of skills appropriate to being military governors of far flung places. This is true, to a lesser extent, of the French. Monty was a disaster as a peacetime administrator, but brilliant at taking the resources he had and crushing an opponent. By contrast, some of the commanders that Monty replaced were superb governors, but not as effective at war fighting. The Americans had their own particular history, which meant that they had excellent theory, but much less experience in war fighting. North America is a long way from the killing fields of Asia and Europe, and most Americans, understandably, wished to keep it that way. Again, success in the American Army did not depend upon your prowess in conquest. The agenda set for Soviet forces was peculiar, especially with Stalin in control, both aggressive and very politically driven. Soviet effectiveness largely affected by a huge theoretical, political gamble.

2. The Germans, by contrast, had one use for their army – conquest. The Prussians had united Germany less than 100 years before by a series of lightning fast political and military actions, and Germany had no tradition of overseas empire building that many of the other European states had. Progress in the German military depended on one thing – your likely success in defeating your immediate European neighbours. They felt that they had nothing to lose. Some of the consequences of this are very ably outlined above.

Germany was fortunate to have a large batch of officers born in the 1890s. These included Rommel, Doenitz, Paulus, Richtofen, Zeitzler, and Dietl. Important "exceptions" such as von Manstein and Guderian were born just a few years earlier, in the late 1880s. In this context, it was important to note that Germany's "maximum leader," Adolf Hitler, was born in 1889, which is to say that these generals were appointed by a "peer." This was known as the "Lost generation," which more than others, had to rely on its own resources.

The reason the 1890s "vintage" was so important was because these men spent their (key) fortysomething age brackets during the 1930s, that is the Global Depression, before ripening into generals around age 50 in the 1940s. These hard economic times shaped an "edgier," more resourceful, more cunning group of officers than the ones that came just before and after them. This was particularly true in Germany, which suffered the double whammy of the depression and the restrictions imposed by the Versailles Treaty. Also, they were much more conversant in the "new" technologies of tanks, airplanes, and self-propelled artillery than older generals of other armies.

America was fortunate to have a number of generals born in the 1890s; Dwight Eisenhower, Omar Bradley, and Mark Clark, who were more adaptable to modern war conditions than older generals such as Patton. These generals were headed by a President (FDR) born in 1882, which may be why there were fewer "1890s"-vintage American generals than Germans.

Britain's commanders (Wavell, Auchinleck, Gort, Montgomery were mostly born in the early to mid-1880s, which is to say in a less timely fashion than the Germans. It is noteworthy that their leader was Winston Churchill, born 1874, who did not appoint brilliant later commanders such as Jock Campbell (born 1894) to senior command.

The French were in the worst shape. Their only general of note born in the 1890s was Charles deGaulle, and he was only a brigadier. Spots ahead of him were occupied by the likes of Generals Gamelin and Weygand, born in the 1860s and 1870s, the right age for World War I (but not II).

There is a fear that today's hard economic times is creating an edgy, hungry, and cunning new "Lost" generation of young adults born in the 1980s and 1990s. (Some would say that the "New Lost" goes back to the 1970s). If there is a major war in the late 2020s, 2030s, or early 2040s, this generation will likely produce the sharpest generals we've seem in modern times; otherwise, they'll become generals of finance, technology, or "cyberwars."

Besides all the very good answers, esp @Tea Drinker, consider survivor bias. Once the war got started, Germany was either going to succeed at first or lose right away. Given their situation, to succeed at first, they needed brilliant generals. If they had not had them, then there wouldn't have been much of a WW2 and those generals wouldn't be talked about.

To go further - to succeed they needed to use effective new tactics, Blitzkrieg in this case, and those new tactics, especially as they are the first to use them, naturally make them look good. And, make no mistake, they are very, very, good.

The fact that they are the first to use Blitzkrieg (which a number of other folks in USA-?, France-De Gaulle, UK-Liddell Hart, and USSR-Tukhachevsky had theorized about as well) has an extra benefit: no other army is ready for the new form of warfare and they have outsized success. Everyone else following in their footsteps will a) not have "invented"* it and b) face much better prepared opponents.

German command doctrine also heavily emphasized initiative by subordinates, which would naturally lead to better senior leaders.

Plus, as the OP wonders, there is a bit of perverse romanticism going on, even though we all know exactly what kinda of beastly system these men were helping with. Germany is the plucky underdog that takes on the whole world. OK, their Nazi component is the rabid plucky underdog that got humanity nearest to pure evil that we've seen, but that's still an effect. You see that all the time with gamers: playing the German side, with its outnumbered super-tanks (which conveniently don't suffer their customary mechanical breakdowns) is quite a bit more popular than one would expect from the Nazi association. Same mechanisms, romanticizing and survivor bias, are at play with Confederate generals like Lee or Stuart - very few people like what the Confederacy fought for, but their military itself is rather impressive, because it had to be for the Civil War to last any length of time.

Note that, either through lack of competence or deliberate post war info management, the Waffen SS generals never quite got the same level of celebrity. In Tank Warfare on the Eastern Front 1941-1942: Schwerpunkt, Robert Forczyk** very emphatically makes the point that the Waffen SS had a negative effect on Wehrmacht performance - they got the best tanks but weren't really good at armored warfare, especially in the beginning, relying on fanaticism and their equipment. Had the regular Army received those troops and tanks instead, they would have been put to better use. By the time the top SS leaders got better at their craft (IF they ever did, compared to the Mansteins and Guderians), Germany's chances of winning had petered out.

* the Germans weren't the only ones thinking of armored breakthroughs, but they were the first to move from theory to practice, which counts for a lot.

** As a side note, Forczyk is less than entirely complimentary about Zhukov, saying that he was really good at getting the best units for his endeavours and at taking credit for his successes (he had to be: there's a bit of literal survivor bias going on with him wrt Stalin purges). He's not saying he was bad, just that he was human too. Ditto his dismissal of Monty.

To my impression this reflects systematic bias of the sources you use, possibly, sources circulating in your country and/or language. In the USSR, for example, there was no such glorification of the German generals, and many of the Soviet marshals and generals (such as Vasilevsky, Rokossovsky, Malinovsky, Konev, Meretskov) were well known.

Today in Russia those Soviet generals are known far less, especially by the younger generation, but the German generals are not known better.