Preheat the oven: Preheat your oven to 350°F (175°C). Lightly grease a standard 12-cup muffin tin, or spray with nonstick cooking spray, so the biscuit cups release easily after baking.
Cook the beef and vegetables: In a large skillet over medium heat, add the ground beef, diced onion, and green bell pepper. Cook, breaking up the beef with a spoon, until the meat is browned and the vegetables are softened. Drain any excess grease if needed.
Add the sloppy joe sauce: Stir in the tomato sauce (or sloppy joe sauce), brown sugar, Worcestershire sauce, garlic powder, salt, and black pepper. Mix well to combine. Let the mixture simmer for 5–7 minutes, stirring occasionally, until thickened and flavorful. Remove from heat and set aside.
Prepare the biscuit cups: Open the can of refrigerated biscuits and separate the dough pieces. Using your hands, gently flatten each biscuit into a round disk. Press each disk into a muffin tin cup, pressing the dough up the sides to create a little biscuit “bowl” for the sloppy joe filling.
Fill with sloppy joe mixture: Spoon the sloppy joe filling into each biscuit cup, dividing it evenly among the muffin cups. Fill almost to the top, but avoid overflowing. Sprinkle shredded cheddar cheese generously over the top of each filled biscuit cup.
Bake the sloppy joe biscuits: Place the muffin tin in the preheated oven and bake for 12–15 minutes, or until the biscuits are puffed and golden brown around the edges and the cheese is melted and bubbly on top.
Cool slightly and serve: Remove the muffin tin from the oven and let the sloppy joe biscuits cool for a few minutes in the pan. Carefully loosen the edges with a knife if needed, then lift each biscuit cup out. Serve warm and enjoy the cheesy, saucy, handheld comfort.