In a large skillet, cook bacon over medium heat until crisp. Remove to paper towel. Drain and discard drippings. Shape beef into four patties. In the same skillet, cook patties over medium heat until no longer pink; cool.
On a lightly floured surface, roll out puff pastry to half of original thickness. Cut into four rectangles. Place slice of mozzarella cheese in the center of each rectangle; top each with four bacon pieces, one beef patty, four more bacon pieces and a slice of cheddar cheese. Wrap pastry around filling. Brush edges with water; seal. Place on a greased baking sheet. Brush with milk. Bake at 425 for 12-15 minutes or until golden brown. Meanwhile, prepare au jus sauce according to package directions. Serve with the burger puffs.