Cook the egg noodles according to package instructions. Drain and set aside.

In a large skillet, heat the vegetable oil over medium-high heat. Add the ground beef and cook until browned, breaking it apart with a spatula, about 5-7 minutes.

Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.

In a small bowl, mix together the soy sauce, brown sugar, rice vinegar, and red pepper flakes. Pour this sauce over the cooked beef and stir to combine.

Add the sliced bell pepper and julienned carrots to the skillet. Cook for another 3-4 minutes until the vegetables are tender but still crisp.

Toss in the cooked egg noodles and chopped green onions, mixing everything well. Season with salt and pepper to taste.

Serve hot, garnished with sesame seeds if desired.