Was there a Japanese Exchange, à la Columbian Exchange?

If you think about it, the cultural exchange is still going on. I can find a sushi place in most any town (in the western US, anyway) - I can even buy pre-made sushi in the supermarket, with California rolls being a staple. Likewise, I can find teriyaki, wasabi, and other Japanese condiments on the shelves. I have a Honda, Toyota, and Mazda in my driveway, at various times have studied judo, kendo, and karate...

It may not be food, but there are quite a few garden plants here on the West Coast of the US that come from Japan originally.

Take a look at Wikipedia:GlossaryOfJapaneseWordsOfDutchOrigin

The Dutch were the first Europeans to start larger scale trading in japan and as such loaned many words for the things they introduced.

At the time there was little reverse trade in 'new' things, it was mostly in either raw materials or crafted items such as laquerware.

The Japanese were never fully isolated from the rest of the world. They're far closer to the Eurasian continent and were not geographically isolated any manner that compares to contact with the Native Americans or the American continent(s).

The Tokugawa Shogunate did restrict trade with the outside world during the Edo period (1603-1868) but they didn't prevent trade, they controlled it. At various times, Dutch, Chinese, and Portuguese merchant had trading ports in Japan, most notably in Nagasaki. The Dutch traders in particular, brought with them technology and knowledge from other European countries, most notably Philipp Franz von Siebold who taught German Medical Science to Japanese students. You can still find German language medical and chemistry textbooks in libraries in Japan (some older physicians still speak German as a result).

As such there was no one intense period of "exchange", the import of European goods, cultures, and technologies was gradual into Japan. They imported them almost continuously from European traders and other merchants in Asia that had contact with the Europeans. Foreigners were not permitted on most of the Japanese islands and Japanese traders gained much of the profits from trading foreign goods within Japan. However, by the time of the arrival of Commodore Matthew Perry (1863) and the Meiji Restoration shortly thereafter, many European goods had already been in Japan for centuries and were not unfamiliar to the Japanese. Dishes such as Castella sponge cake (from Portugal), Ramen noodles and Gyoza dumplings (from China), and Curry (based on Anglo-Indian cuisine) are widely regarded as traditional foods in Japan rather than foreign (with many local variations). Today there are Japanese derivations of almost any foreign food, including unique pasta recipes and bakeries that incorporate unique Japanese products (such as An red bean paste, mentaiko, and matcha green tea).

Conversely, there were not as many imports to Europe from Japan as there were from the Americas either. Europeans never occupied and controlled the Japanese islands, nor did they have any need to. Due to geographical proximity and trade with other countries in the region, Europeans could already get food crops such as Rice from other countries. Most notably, trade and colonies in China, India, and Indonesia provided many similar crops, tea, and spices (which were more lucrative).

The uniqueness of Japanese cuisine is not due to the differences in local flora, fauna, or geography. Many of the same foods can be found on islands with similar climates. It is due to differences in culture. It takes a high level of training and craftsmanship to produce many Japanese products (including foods rich in "umami"). Without the demands of a local market, these have been uneconomical to produce in the rest of the world until recently. Many items produced by the Japanese (such as knives) are still highly prized in other countries for their quality but cannot be reproduced in the same manner as, say, growing a potato, so they've largely remained in Japan (and the recent diaspora). There were likely plenty of similarly unique cultural practices in Native American societies but the European settlers took little notice of these as they were more interest in the natural resources (such as land, gold, and silver) in the Americas.

Adding to Semaphore's good answer, other products introduced in Japan after European contact were wine and opium.

Wine has been imported into the archipel since the 15th century.

Both wine and opium have been documented to have been produced in Japan as early as 1627 and 1629 respectively.

Japan would later take a major role in the trade of opium in the second half of the 19th century.

At least two of the new crops introduced by the Portugese in the early 1600s had major social and economic impacts in Japan.

Sweet Potato

As with white potatoes, they were first introduced by the Portugese in 1605, and were initially fed only to horses. A few decades later they started to be accepted as food and by 1735, the Tokogawa shogun planted them in his own palace garden. A gruel made with sweet potato became "a standard banquet dish" for the aristocracy.

I think it would be fair to say that sweet potatoes actually became a staple food, although obviously not on the same level with rice. By the early eighteenth century they were an important source of calories and a "bulwark against famine", especially in dry upland areas of western Japan where rice was not as productive. This likely contributed to the rapidly increasing population and urbanization of the period.

Cotton

Prior to extensive contact with the Portugese, cotton was an expensive, imported luxury item that could make the silk garments of the upper classes a bit warmer. That began to change as "the seeds of cotton introduced by Portuguese had swiftly spread throughout the whole country". Young women began to spin cotton for sale, increasing the cash income of peasant households.

Cotton replaced hemp as the main fiber available to the common people, which "transformed clothing and bedding... and in so doing dramatically increased the quality of life." In western Japan, cloth bedding was apparently so scarce that as late as 1789, "people dried seaweed and wove it into quilts" to keep themselves warm at night!

Cottonseed oil also helped to make lamp oil for lighting much more affordable and widely available in the 1600s then it had been before. Osaka became a center of production, both for cotton textiles and for lamp oil.