In a medium skillet over medium-high heat, add the ground beef and cook, breaking it apart with a spatula, until browned, about 5–7 minutes.

Reduce heat to medium, stir in the chopped onion and minced garlic, and cook for 3–5 minutes until the onion is translucent.

Incorporate salt, pepper, Worcestershire sauce, and beef broth, stirring well. Simmer for 5–7 minutes until the sauce thickens.

Spread unsalted butter on one side of each slice of bread. Preheat a skillet or griddle over medium heat.

On the non-buttered side of one slice, layer half of the cheddar cheese, then spoon the beef mixture on top, followed by the remaining cheese. Top with another slice of bread.

Carefully transfer the assembled sandwich to the skillet and grill for about 3–4 minutes per side.

Once grilled to perfection, remove from skillet, let cool slightly, slice in half, and serve.