Heat olive oil in a large skillet or sauté pan over medium-high heat. Add the ground beef and cook, breaking it apart with a wooden spoon, until fully browned and no pink remains, about 6 to 7 minutes. Drain excess fat from the pan, leaving about 1 tablespoon behind for flavor.

Push the beef to one side of the pan. Add the diced onion and green bell pepper to the empty side and cook, stirring, for 3 to 4 minutes until softened. Add the minced garlic and cook 30 seconds more until fragrant. Stir everything together.

Add the tomato paste directly to the pan. Stir it into the meat and vegetables and let it cook for 1 to 2 minutes, stirring frequently — this cooks off the raw tomato flavor and deepens the sauce's richness.

Pour in the beef broth and scrape up any browned bits from the bottom of the pan. Add the ketchup, Worcestershire sauce, brown sugar, apple cider vinegar, yellow mustard, smoked paprika, cayenne (if using), salt, and black pepper. Stir to combine thoroughly.

Reduce the heat to medium-low and let the mixture simmer uncovered, stirring occasionally, for 8 to 10 minutes until the sauce has thickened and clings to the meat. Taste and adjust seasoning — add more brown sugar for sweetness, vinegar for tang, or salt as needed.

While the filling simmers, butter the cut sides of your buns and toast them in a separate skillet over medium heat or under the broiler until golden brown.

Spoon the sloppy joe filling generously onto the toasted buns. Top with pickle slices if desired and serve immediately.