Heat olive oil in a medium skillet over medium heat.
Add chopped onion and green bell pepper; sauté for 3 to 4 minutes until softened.
Add minced garlic and cook for 30 seconds until fragrant.
Add ground beef to the skillet; cook, breaking it up with a spoon, until browned and cooked through, about 5 to 6 minutes.
Stir in tomato sauce, ketchup, Worcestershire sauce, brown sugar, chili powder, salt, and black pepper.
Simmer the mixture for 5 minutes, stirring occasionally, until thickened. Remove from heat.
Preheat a large skillet or griddle over medium heat.
Butter one side of each slice of bread.
Place 4 slices of bread, buttered side down, on the skillet.
Layer each slice with 2 slices of cheddar cheese, then evenly spoon the sloppy joe mixture over the cheese.
Top the sloppy joe mixture with another 2 slices of cheddar cheese on each sandwich.
Place the remaining 4 slices of bread on top, buttered side up.
Cook the sandwiches for 3 to 4 minutes on each side, pressing gently with a spatula, until the bread is golden brown and the cheese is melted.
Remove sandwiches from skillet, let cool for 1 minute, then slice in half and serve.