Begin by cooking the egg noodles according to package instructions. Drain and set aside.
In a large skillet or wok, heat the vegetable oil over medium-high heat.
Add the chopped onion and sauté for 2-3 minutes until translucent, then add minced garlic and grated ginger. Stir for about 1 minute until fragrant.
Push the onion mixture to one side of the skillet and add the ground beef. Cook until browned and fully cooked, breaking it apart with a spatula (about 5-7 minutes).
Stir in the sliced bell peppers, broccoli florets, and snap peas. Cook for an additional 4-5 minutes until vegetables are tender-crisp.
In a small bowl, whisk together the soy sauce, hoisin sauce, sesame oil, brown sugar, and red pepper flakes. Pour this sauce over the beef and vegetables, stirring to coat everything evenly.
Add the cooked egg noodles to the skillet. Toss everything together until the noodles are heated through and well mixed with the sauce (about 2 minutes).
Remove from heat and adjust seasoning with additional soy sauce if desired.
Notes
Serve in large bowls, garnished with green onions and sesame seeds.