Spread dressing evenly on 1 side of each bread slice. Layer 6 rye bread slices and 6 pumpernickel bread slices evenly with cheese, sauerkraut mixture, and corned beef. Stack to make 6 (2-layer) sandwiches, ending with remaining rye bread slices.
Coat a baking sheet with vegetable cooking spray, and arrange sandwiches on baking sheet. Coat bottom of a second baking sheet with cooking spray, and place, coated side down, on top of corned beef sandwiches.
Bake sandwiches at 475° for 15 to 20 minutes or until golden and cheese is slightly melted. Serve warm.