Cook the egg noodles according to package instructions until al dente. Drain and set aside.
In a small bowl, whisk together soy sauce, oyster sauce, hoisin sauce, toasted sesame oil, beef broth, and cornstarch until smooth. Set the sauce mixture aside.
Heat vegetable oil in a large skillet or wok over medium-high heat.
Season the sliced beef with salt and black pepper.
Add the beef to the skillet and stir-fry for 3-4 minutes until browned but not fully cooked. Remove the beef from the skillet and set aside.
In the same skillet, add the minced garlic and ginger and stir-fry for 30 seconds until fragrant.
Add the broccoli florets, julienned carrot, red bell pepper, and snap peas to the skillet. Stir-fry for 4-5 minutes until the vegetables are crisp-tender.
Push the vegetables to one side of the skillet. Pour the beaten egg into the empty side and scramble it until just set, about 1-2 minutes.
Return the beef to the skillet along with the cooked noodles and pour the prepared sauce over everything.
Toss all ingredients together and stir-fry for an additional 2-3 minutes until the beef is cooked through and the sauce thickens.
Remove from heat and stir in the sliced green onions.
Serve hot.