In a large skillet over medium-high heat, add the ground beef to the skillet. Cook for 6-8 minutes or until browned, breaking up the ground beef with a spatula.
Add onions, green peppers, and garlic. Cook for 4-5 minutes or until they become soft.
Add tomato sauce, ketchup, brown sugar, yellow mustard, chili powder, Worcestershire sauce, black pepper, salt, onion powder, and paprika to the ground beef and veggies. Mix until well combined and cook for 4-5 minutes, stirring occasionally.
Butter one side of each piece of Texas toast with ½ tablespoon of butter.
Heat griddle or skillet over medium heat. Place two pieces of toast, butter side down, in the griddle or skillet. Place one slice of muenster cheese on one piece of bread. Then place one slice of cheddar cheese on the other piece of bread.
Add ¼ of the sloppy joe mixture to one slice of bread. When the cheese starts to melt. Top the sandwich with the other piece of bread. Flip and cook until cheese is completely melted.