In a large bowl, combine the ground beef, Worcestershire sauce, salt, and pepper. Mix well until evenly seasoned.

Divide the seasoned beef into 6 portions and shape each portion into a patty that matches the size of the bread slices.

Heat a skillet or griddle over medium-high heat. Cook the patties for 4-5 minutes per side, or until your desired doneness. Set aside.

Butter one side of each slice of marble rye bread.

Toast the bread, buttered side down, in the skillet or griddle until golden brown (about 2-3 minutes per side).

Once the bread is toasted, place a patty on the unbuttered side of 6 slices of bread.

Top each patty with a slice of your chosen cheese, then cover with the remaining bread slices, buttered side facing out.

Grill the sandwiches for an additional 2-3 minutes per side, pressing gently with a spatula, until the cheese is melted and the bread is crispy.

Remove from the skillet, cut in half, and serve hot with your favorite dipping sauce (optional).