Saute onion, bell pepper, and garlic in vegetable oil in a large skillet over medium heat. Stir frequently to prevent burning.
Add ground beef and brown until fully cooked. Add diced tomatoes, tomato sauce, brown sugar, Worcestershire sauce, apple cider vinegar, and hot sauce.
Stir to thoroughly combine and add in egg noodles. Cover and cook until noodles are tender but not overcooked, about 6-8 minutes.
Season with salt and pepper and top with shredded cheese.