Fill a large pot 3/4 full with water and bring to a boil. Add the noodles and cook until tender, 5 to 6 minutes, or according to the package directions. Drain and rinse the noodles thoroughly with cold water. Set aside.
In a large pot or frying pan, heat the oils over medium heat. Add ginger and garlic and stir-fry until fragrant. Stir in the soy sauce and broccoli and continue to cook over medium heat for about 3 minutes. Add remaining vegetables and cooked noodles, and toss until warmed through.
Divide the noodles among warmed plates and top with crushed red chili flakes, if desired. Serve immediately.