Brown the beef: Heat a large skillet over medium-high heat and add the ground beef, breaking it into small crumbles with a spatula. Cook until no pink remains, about 6 minutes.
Drain excess grease: Tilt the skillet and spoon off any extra fat so the sauce doesn't turn greasy. Leave just enough to keep the pan lightly coated.
Cook onion and pepper: Add the diced onion and bell pepper to the skillet and cook over medium heat until softened, about 4 minutes. Stir occasionally so they cook evenly.
Add the garlic: Stir in the minced garlic and cook just until fragrant, about 30 seconds. Watch it closely so it doesn't burn.
Build the sauce: Pour in the ketchup, brown sugar, Worcestershire sauce, mustard and water. Stir everything together until the meat is evenly coated in a glossy sauce.
Season to taste: Add salt and black pepper, tasting as you go. Adjust the sweetness or tang with a touch more brown sugar or mustard if needed.
Simmer until thick: Reduce the heat to low and let the mixture simmer uncovered, stirring occasionally, until it thickens and clings loosely to the spoon, about 10 minutes.
Toast the buns: While the sauce simmers, toast the hamburger buns lightly in a dry skillet or under the broiler for about 1 minute, until the edges turn golden.
Assemble and serve: Spoon the warm beef mixture generously onto the bottom half of each bun. Top with the other half and serve immediately while hot.