01 - Heat olive oil in a large skillet over medium heat if using. Add ground beef and cook, breaking up with a spoon, until browned and no longer pink, about 5 minutes. Drain excess fat if necessary.
02 - Add onion, bell pepper, and garlic to the skillet. Sauté for 4-5 minutes until vegetables are softened and fragrant.
03 - Stir in tomato sauce, tomato paste, ketchup, Worcestershire sauce, brown sugar, mustard, smoked paprika, chili powder, salt, pepper, and water. Mix thoroughly until well combined.
04 - Reduce heat to low and simmer, uncovered, for 10-12 minutes, stirring occasionally, until the mixture has thickened to a hearty consistency.
05 - Meanwhile, heat a large skillet or griddle over medium heat. Spread butter on the cut sides of the buns and toast, cut side down, until golden and crisp, 2-3 minutes.
06 - Spoon the sloppy joe mixture generously onto the toasted buns. Serve immediately while hot.