In a large pot of boiling salted water, cook noodles until tender to the bite, about 7 minutes. Drain, rinse well in cold running water and drain again. Toss with sesame oil. Transfer to a serving bowl or deep platter and set aside.

Broccoli Sauce: In a small bowl, combine soy sauce, sake, cornstarch, sugar, chili sauce and pepper to taste. Mix well and set aside.

In a skillet or wok, heat oil over medium heat for 30 seconds. Add garlic and ginger and cook, stirring, for 1 minute. Add broccoli and toss to coat. Sprinkle with stock. Reduce heat to low. Cover and cook until broccoli is tender, about 5 minutes. Add soy sauce mixture and cook, stirring, until thickened, about 30 seconds.

Arrange broccoli mixture over noodles, sprinkle with green onions and drizzle with sesame oil. Serve immediately or let cool to room temperature.