Bring a large pot of lightly salted water to a boil. Cook soba in boiling water, stirring occasionally, until noodles are tender yet firm to the bite, 5 to 6 minutes. Drain.

Heat oil in a large skillet over medium heat. Add onion and garlic and stir-fry for 1 minute. Toss in mushrooms and eggplant; cook for 2 minutes more. Add cooked soba noodles, bok choy, soy sauce, teriyaki sauce, and pepper. Cook until bok choy is tender, about 2 minutes.

Sprinkle sesame oil and green onion over vegetables and serve.