Sloppy Joe Grilled Cheese

In a large skillet over medium heat, heat oil. Add onion and cook, stirring, until soft, about 5 minutes. Add ground beef and cook, stirring and breaking up meat, until no longer pink, 6 to 8 minutes. Drain fat. Return beef mixture to skillet over medium heat and stir in ketchup, garlic, brown sugar, mustard, and chili powder and season with salt and pepper. Simmer until thick, 5 minutes. Transfer mixture to a plate and wipe skillet clean. Assemble sandwiches: Butter one side of each bread slice. Place 1 slice butter-side down in skillet and spoon over sloppy joe mixture. Top with cup of cheddar cheese and one more slice bread, buttered-side up. Cook over medium heat until bread is golden and cheese is melty, about 3 minutes per side. Repeat with remaining ingredients to make 4 sandwiches total.