Heat a skillet over medium heat. Add the ground beef and cook until browned, about 5 to 7 minutes. Break it up as it cooks and drain extra grease if needed.

Add the diced onion and bell pepper. Cook for about 4 to 5 minutes until they soften. Add the minced garlic and cook for 1 more minute.

Stir in the ketchup, tomato paste, Worcestershire sauce, yellow mustard, and brown sugar. Mix well until combined. Let it simmer over low heat for 10 minutes until thickened. Season with salt and black pepper to taste.

Split the hamburger buns and toast them lightly in a skillet with butter for about 1 minute per side.

Spoon the sloppy joe mixture onto the toasted buns, cover with the top bun, and serve immediately with napkins.