Brown beef, onion and bell pepper in a large skillet over medium-high heat for 7 to 8 minutes, breaking the meat into fine crumbles, until the beef reaches 160°F. Drain excess fat if present.
Stir in garlic for 30 seconds, then add ketchup, tomato paste, brown sugar, vinegar, Worcestershire, mustard, water, salt and pepper.
Simmer uncovered over medium-low heat for 10 to 12 minutes, stirring, until the sauce clings to the beef and a spoon leaves a brief path across the skillet.
Butter the cut sides of the buns and toast them in a dry skillet for 1 to 2 minutes until lightly golden.
Divide the hot filling among the toasted buns and serve immediately.