In a medium-sized skillet add the olive oil and onion over medium-high heat. Sauté until almost tender and add the ground beef and cook and crumble until no longer pink.
Add the garlic, ketchup, brown sugar, chili powder, paprika, Worcestershire sauce salt, and pepper. Let simmer for 2-3 minutes.
Making the grilled cheese:
To assemble the grilled cheese: Combine the butter and mayonnaise and spread on the outside of the bread. Lay the bread butter side down in a medium-sized skillet. Sprinkle cheese on top of the bread. Put about 1/4 cup meat mixture on top of the cheese, sprinkle cheese on top of the meat and then top with the other slice of bread.
Cook for about 2-3 minutes over medium-high heat, flip to the other side and continue to cook until golden brown and heated throughout.