For sauce, in a small bowl stir together soy sauce, sugar, and sesame oil. Set aside.
Pour cooking oil into a wok or 12-inch skillet. (Add more oil as necessary during cooking.) Preheat over medium-high heat. Stir-fry ginger and garlic in hot oil for 15 seconds. Add broccoli and asparagus; stir-fry about 4 minutes or until vegetables are crisp-tender. Remove broccoli mixture from the wok.
Add squash, mushrooms, and sesame seed to the hot wok; stir fry for 2 to 3 minutes or until crisp-tender. Return broccoli mixture to the wok. Add green onions.
Pour sauce over vegetables. Cook and stir for 1 to 2 minutes more or until heated through. Serve immediately. Makes 4 to 6 side-dish servings.