Warm the oil in a large skillet over medium heat.
Sauté the onion and bell pepper until softened, about 4 minutes.
Add the ground beef. Cook, breaking it up, until browned. Drain excess fat if needed.
Stir in the garlic and cook until fragrant, about 30 seconds.
Pour in tomato sauce, ketchup, and water. Whisk in tomato paste until smooth.
Season with Worcestershire, mustard, brown sugar, vinegar, chili powder, paprika, salt, and pepper.
Simmer uncovered, stirring occasionally, until thick and glossy, 8–12 minutes.
Taste and adjust seasoning. Add a splash of water if too thick. Serve on toasted buns.