Heat olive oil in a medium skillet over medium heat.
Add the chopped onion and green bell pepper to the skillet and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the ground beef to the skillet and cook until browned, breaking it apart with a spoon, about 5-6 minutes.
Drain any excess fat from the skillet.
Stir in the 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 clean 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 with one slice of cheddar cheese, followed by about 1/4 cup of the sloppy joe mixture, then another slice of cheddar cheese.
Top with the remaining bread slices, buttered side up.
Cook sandwiches for 3-4 minutes on each side, pressing gently with a spatula, until the bread is golden brown and the cheese is melted.
Remove from skillet, let cool for 1 minute, then slice and serve.