Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it up with a wooden spoon, until mostly browned, about 5 minutes. Add the diced onion and bell pepper and continue cooking until the vegetables soften and the beef is fully browned, about 4 minutes more. Drain excess fat if needed.

Stir in the tomato sauce, ketchup, Worcestershire sauce, brown sugar, smoked paprika, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Reduce heat to medium-low and simmer, stirring occasionally, until the sauce thickens and clings to the meat, about 10 minutes. Taste and adjust seasoning.

While the filling simmers, preheat your oven to 400 degrees F. In a small bowl, mash together the softened butter, minced garlic, and dried parsley until well combined.

Spread the garlic butter evenly over the cut sides of the French bread. Place on a baking sheet, buttered side up. Bake until the edges are golden and crisp, about 8 to 10 minutes. If using Parmesan, sprinkle it on during the last 2 minutes of baking.

Spoon the hot sloppy joe filling generously over the toasted garlic bread halves. Cut each half into 2 or 3 pieces and serve immediately, with plenty of napkins.