Prepare all your ingredients by measuring out the egg noodles, soy sauce, and other sauces. Chop the green onions, slice the bell peppers, and julienne the carrots. Mince the garlic and grate the ginger.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the ground beef and cook for about 5-7 minutes until browned.
Add the minced garlic and grated ginger to the skillet and cook for an additional 1-2 minutes until fragrant. Pour in the soy sauce, brown sugar, rice vinegar, and red pepper flakes. Stir to coat the beef.
Add the chopped green onions, sliced bell pepper, and julienned carrots. Cook for another 3-5 minutes, stirring frequently until the vegetables are tender yet crisp.
Prepare the egg noodles according to the package instructions. Drain and set aside.
Toss the cooked egg noodles into the skillet with the beef and vegetable mixture. Mix until the noodles are well coated with the sauce. Season with salt and pepper as needed.