Begin by cooking the egg noodles according to package instructions. Drain and set aside.
In a large skillet or wok, heat 2 tablespoons of vegetable oil over medium-high heat.
Add the ground beef to the skillet and cook, stirring frequently, until browned and cooked through (about 5-7 minutes). Drain excess fat if necessary.
Add the diced onion and minced garlic to the skillet. Stir and cook for about 2-3 minutes, until the onion is translucent.
Incorporate the sliced bell pepper, broccoli florets, and julienned carrots into the skillet. Stir and cook for an additional 5 minutes, until the vegetables are tender-crisp.
In a small bowl, mix together the soy sauce, hoisin sauce, sesame oil, ground ginger, and black pepper. Pour this sauce over the beef and vegetables, stirring to combine.
Add the cooked noodles to the skillet and toss everything together gently until the noodles are well-coated with the sauce.
Remove from heat and garnish with chopped green onions and sesame seeds if desired. Serve warm.