Bring a medium pot of salted water to a boil. Add the egg noodles and cook according to package instructions until al dente. Drain and set aside.
In a large skillet or frying pan, heat the vegetable oil over medium-high heat. Add the sliced beef and season with salt and pepper. Cook for about 5-7 minutes, stirring occasionally, until browned and cooked through. Remove beef from the skillet and set aside.
In the same skillet, add the chopped onion and minced garlic. Sauté for about 3-4 minutes until the onion is translucent.
In a mixing bowl, combine the beef broth, soy sauce, cornstarch, brown sugar, and ground ginger. Stir until the cornstarch is fully dissolved.
Pour the sauce mixture into the skillet with the onions and garlic. Bring to a simmer and cook for 3-4 minutes, allowing the sauce to thicken.
Add the cooked beef, mixed vegetables, and cooked noodles to the skillet. Toss everything together gently to ensure the beef, noodles, and vegetables are evenly coated in the sauce. Cook for an additional 2-3 minutes until heated through.
Remove from heat and garnish with sliced green onions before serving.