Melt 1 teaspoon butter in a large nonstick skillet coated with cooking spray over medium-high heat. Add onion, and cook for 4 minutes or until golden brown, stirring frequently. Reduce heat; cook 10 minutes or until tender, stirring occasionally. Set aside.
Combine beef, pepper, and salt in a medium bowl. Divide the beef mixture into 4 equal portions, shaping each into a 1/4-inch-thick oval patty. Place the patties on a broiler pan coated with cooking spray; broil 4 minutes on each side or until done.
Place 1 cheese slice over each of 4 bread slices; top each slice with 1 patty and 3 tablespoons onion mixture. Cover with the remaining bread slices. Melt 1/2 teaspoon butter in pan coated with cooking spray over medium heat; add 2 sandwiches to pan. Cook for 4 minutes on each side until browned and cheese melts. Repeat the procedure with 1/2 teaspoon butter and the remaining sandwiches.