Brush melted butter evenly on 1 side of 16 bread slices. Place, butter sides down, on wax paper.
Sprinkle 1 Tbsp. Swiss cheese on top of each of 8 bread slices; top evenly with chicken, tomato slices, and 1 cup warm White Cheese Sauce. Sprinkle with bacon and remaining cheese, and top with remaining bread slices, butter sides up.
Cook sandwiches, in batches, in a preheated panini press 2 to 3 minutes or until golden brown. Serve with remaining 2 cups warm White Cheese Sauce for dipping.