Heat a skillet over medium. Add the ground beef, chopped onion, and minced garlic. Break the beef into small pieces and cook, stirring occasionally, until the beef is evenly browned and the onion is translucent, about 6 to 8 minutes.

Sprinkle in the salt, black pepper, and paprika. Stir, taste, and adjust seasoning. Remove the skillet from heat and set the beef mixture aside.

Spread softened butter evenly on one side of each bread slice.

Place one slice of bread, buttered side down, in a clean skillet preheated to medium.

Pile half of the beef mixture onto the bread in the skillet. Arrange two slices of cheese over the hot beef.

Top with the second slice of bread, buttered side up. Cook until the bottom is golden brown, about 3 to 4 minutes.

Flip the sandwich carefully and cook until the second side is golden and the cheese is fully melted, another 3 to 4 minutes. Reduce the heat if the bread browns faster than the cheese melts.

Transfer the sandwich to a cutting board. Let it rest for 1 minute, then slice and serve warm with optional lettuce, tomato, or pickles.