Warm a large skillet over medium heat and melt the butter.
Sauté the onion and bell pepper until softened, about 5–6 minutes.
Stir in the garlic, chili powder, and smoked paprika; cook 30 seconds until fragrant.
Add the ground beef, breaking it up as it cooks; brown until no pink remains, then drain excess fat.
Mix in ketchup, tomato sauce, brown sugar, mustard, Worcestershire, vinegar, water, salt, and pepper.
Simmer uncovered, stirring occasionally, until thick and glossy, 8–10 minutes. Adjust seasoning to taste.
Lightly toast the buns in a dry skillet or under the broiler until golden.
Spoon the hot mixture onto the buns and serve right away.