Preheat oven to 350°. In a large skillet, cook beef and onion over medium heat until the meat is no longer pink; drain. Stir in tomato sauce, mushrooms, parsley, salt, oregano and pepper; set aside.
Unroll 1 tube of crescent dough and separate dough into eight triangles. Arrange in a single layer in a lightly greased 9-in. pie plate. Press into dish to form a crust and seal seams. In a small bowl, whisk eggs and 1 egg white.
Pour half of beaten egg mixture over pie shell. Spoon meat mixture into shell; arrange cheese slices on top. Spread with remaining beaten egg. Mix water and remaining egg yolk; set aside.
Unroll second tube of crescent dough; place four sections of dough together to form a 12-in. x 6-in. rectangle. Press perforations to seal; roll dough into a 12-in. square.
Brush edges of bottom crust with some of the egg yolk mixture; place dough on top of filling. Trim, seal and flute edges. Cut slits in top. Brush top with remaining egg yolk mixture.
Bake for 40 minutes, tenting with foil after 15 minutes if necessary. Let stand for 10 minutes before serving.