In a large skillet over medium-high heat, saute beef, onion, broccoli, and sweet pepper in oil, stirring occasionally until beef is browned and vegetables are just tender. Add garlic and saute 1 additional minute until fragrant. Remove from heat.
In a small bowl, whisk soy sauce, vinegar, water, sugar, ginger, and cornstarch/water mixture until smooth. Return pan of vegetables and beef to medium heat and add sauce to pan. Cook several minutes, stirring occasionally until sauce is slightly thickened.
Stir noodles into sauce mixture until evenly coated. Season with salt and pepper to taste. Top noodles with green onions and serve warm. Enjoy!