Preheat your oven to 375°F.
In a small bowl, mix the softened butter, minced garlic, dried parsley, and salt until well combined.
Slice the French bread loaves in half lengthwise and place them on a baking sheet, cut side up. Spread the garlic butter mixture evenly over the cut sides of the bread.
In a large skillet over medium heat, cook the ground beef, onion, and green bell pepper until the beef is browned and the vegetables are tender, about 5-7 minutes. Drain any excess fat.
Stir in the ketchup, Worcestershire sauce, brown sugar, and mustard. Simmer for 5 minutes, allowing the flavors to meld.
Spoon the sloppy joe mixture generously over the garlic buttered bread halves. Top with shredded cheddar cheese.
Bake in the preheated oven for 15-20 minutes, or until the cheese is melted and bubbly and the edges of the bread are golden brown.
Remove from the oven and let cool for a few minutes before slicing. Serve warm.