Cook the noodles: Cook the noodles according to the package instructions. Drain and set aside.
Heat the oil: Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the onion and garlic: Add the diced onion and minced garlic to the skillet and cook until the onion is translucent.
Add the ground beef: Add the ground beef to the skillet and cook until it is browned, breaking it up into small pieces as it cooks.
Add the mushrooms and snow peas: Add the mixed mushrooms and sliced snow peas to the skillet and cook until the vegetables are tender-crisp.
Add the beef broth and sauces: Add the beef broth, soy sauce, oyster sauce (if using), hoisin sauce, grated ginger, and red pepper flakes to the skillet. Stir to combine.
Simmer the sauce: Simmer the sauce for 2-3 minutes, or until it has thickened slightly.
Add the noodles: Add the cooked noodles to the skillet and stir to combine with the sauce.
Season with salt and pepper: Season the noodles with salt and pepper to taste.
Serve: Serve the Mongolian Ground Beef Noodles hot, garnished with chopped scallions (if desired).