Heat the skillet: Warm the olive oil in a large skillet over medium-high heat until it shimmers. This keeps the beef from sticking as it starts to brown.

Brown the beef: Add the ground beef, onion, and bell pepper, breaking the meat into small crumbles with a spoon. Cook for about 7 minutes, until no pink remains and the onion softens.

Drain excess fat: Tilt the skillet and spoon off any extra grease. This keeps the final sauce from turning oily instead of thick.

Add garlic: Stir in the minced garlic and cook for about 30 seconds, just until fragrant. Watch closely so it doesn't burn.

Stir in the sauce base: Add the ketchup, brown sugar, tomato paste, Worcestershire sauce, and mustard. Stir until the mixture turns a deep, glossy red and coats the meat evenly.

Season the sauce: Sprinkle in the chili powder and smoked paprika, then season with salt and pepper. Stir well so the spices distribute evenly through the meat.

Add broth and simmer: Pour in the beef broth and lower the heat to medium-low. Let the sauce simmer uncovered for 12 to 15 minutes, stirring occasionally.

Check the texture: The sauce is ready when it coats the back of a spoon and no longer looks watery. If it's too thick, add a splash more broth.

Toast the buns: While the sauce finishes simmering, toast the hamburger buns lightly in a dry pan or under the broiler until golden at the edges.

Assemble and serve: Spoon the hot sloppy joe mixture generously onto the toasted buns. Serve right away while the sauce is still warm and glossy.