3 tablespoons sesame seeds
1/4 cup Asian sesame oil
1/4 cup mirin (sweet Japanese rice wine)*
3 tablespoons soy sauce
3 tablespoons (packed) golden brown sugar
2 tablespoons oyster sauce*
10 green onions, chopped
6 ounces fresh shiitake mushrooms, stemmed, caps cut into 1/3-inch-thick slices
1 pound choy sum or baby bok choy, just enough of bottoms cut off to separate stalks; stalks and leaves cut crosswise into 2-inch-wide strips
1/4 pound snow peas (strings removed), cut in half lengthwise
1 medium carrot, peeled, cut into matchstick-size strips (about 1 cup)
8 ounces Chinese vermicelli with sweet potato starch
3 tablespoons vegetable oil, divided
3 large shallots, sliced into thin rounds, divided
Stir sesame seeds in heavy medium skillet over medium-low heat until lightly toasted, about 4 minutes. Transfer to small dish.
Mix next 5 ingredients in small bowl. Stir in green onions and 2 tablespoons toasted sesame seeds; season with salt and pepper. Transfer 3 tablespoons sauce to medium bowl and mix in mushrooms; marinate 15 minutes.
Blanch choy sum, snow peas, and carrot in large pot of boiling salted water 1 minute. Using strainer, transfer vegetables to colander. Rinse with cold water and set aside to drain. Return water to boil; add noodles. Cook until just tender but still slightly chewy, stirring often, about 4 minutes. Drain, rinse with cold water, and drain again. Using kitchen shears, cut noodles crosswise in several places. (Sauce, mushrooms, vegetables, and noodles can be prepared 2 hours ahead. Let stand at room temperature.)
Heat 1 tablespoon vegetable oil in heavy large nonstick skillet over medium-high heat. Add half of shallots; stir 30 seconds. Add mushroom mixture; sauté until tender, about 4 minutes. Scrape mushroom mixture into large bowl. Heat 2 tablespoons oil in same skillet over medium heat. Add remaining shallots and stir 30 seconds. Add remaining sauce and noodles. Simmer until noodles absorb almost all sauce, stirring often, about 5 minutes. Add noodle mixture to bowl with mushrooms. Add choy sum, snow peas, and carrot; toss. Season with salt and pepper.
Transfer stir-fry to large shallow bowl. Sprinkle with remaining 1 tablespoon sesame seeds and serve.