I used a paste made from wasabi powder for this dish and made it up using a little soy sauce. The onions were delicious but a little salty, next time I will try using sweet soy. I used missy preferred method of no oil and It worked fine, I let mine cook down until they were getting sticky and burnt yum!
I used more than the wasabi called for (and it was restaurant quality) but it seemed to disappear in the pan. When the onions were done, I tasted it and I ended up adding soy sauce and more wasabi--that did the trick! Next time I'll try making a paste of soy sauce and wasabi and frying the onions in that, so it sticks. The flavor combination is yummy--like sushi without the fish. Would be nice served over rice.