Bring a large pot of water to boil. Add the noodles and cook until al dente (tender), 10 to 12 minutes, or according to the package directions. Drain the noodles thoroughly. Set aside.
In a large pot or 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.
Serve topped with crushed red chili flakes (optional).