Place 1/4 cup cheese 4 of the bread slices. Divide bacon, tomato and avocado evenly onto bread. Top with remaining cheese and bread slices. Spread 2 teaspoons butter over each top slice of bread.
Heat a large skillet over medium heat. Place sandwiches, buttered side down. Spread remaining butter over top slices of bread. Cook uncovered about 5 minutes or until bottoms are golden brown. Turn; cook 2 to 3 minutes longer or until bottoms are golden brown and cheese is melted.