Cook noodles according to package directions. Drain and rinse under cold water. Set aside.
Grate tofu over large holes of box grater.
In large skillet over medium, heat oil. Add mushrooms and heat until softened, about 3 minutes. Add spring onion whites, garlic, ginger, and chili sauce to pan; heat for 30 seconds. Add crumbled tofu and cook for 5 minutes. Add broth, tamari or soy sauce, and sugar; bring to a simmer.
In small bowl, mix cornstarch with 1 Tbsp water and add to pan. Cook, stirring frequently, until slightly thickened, about 1 minute. Stir in reserved noodles and watercress; heat for 1 minute.
Divide among serving bowls and serve topped with onion greens, cilantro, and sesame seeds. Serve with lime wedges.