Bring a large pot of heavily salted water to a boil. Add noodles and cook according to package directions. Add broccoli to the pot for the last five minutes. Add peas to the pot just before draining. Drain and set aside.
Make the sauce by mixing hoisin sauce, broth, soy sauce, and chili-garlic sauce in a small bowl. Set aside.
In a large skillet, heat oil over medium-high heat and saute onion, mushrooms, and carrot until soft and lightly browned. Add scallions, ginger, and coriander; cook a few more minutes until fragrant.
Add cooked noodles, broccoli, and peas and let cook a couple of minutes. Add bean sprouts and sauce. Let cook, stirring constantly, until pasta is heated through and coated with sauce. Season if needed and serve immediately.