Cook 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 sliced beef and stir-fry for about 3-4 minutes until browned.

Add the bell peppers, onions, shredded carrots, garlic, and ginger to the skillet. Stir-fry for an additional 3-5 minutes until the vegetables are tender-crisp.

In a small bowl, mix together the soy sauce, hoisin sauce, sesame oil, and red pepper flakes (if using). Pour this sauce over the beef and vegetable mixture, stirring to combine.

Add the cooked egg noodles to the skillet and toss everything together until the noodles are heated through and well coated with the sauce.

Remove from heat and garnish with chopped green onions and sesame seeds before serving.