Cook the noodles according to package instructions, drain, and set aside.
Whisk together all the sauce ingredients in a small bowl.
Heat vegetable oil in a large skillet or wok over medium-high heat.
Add garlic and ginger and sauté for 30 seconds.
Add carrots, broccoli, mushrooms, and bell peppers. Stir-fry for 2–3 minutes.
Add cabbage and green onions and cook for another 1–2 minutes.
Add cooked noodles and pour the prepared sauce over everything.
Toss thoroughly and cook for 2–3 minutes until the noodles are evenly coated.
Garnish with sesame seeds and extra green onions.
Serve immediately.