Preheat oven to 350°.
Coat a 13 x 9-inch baking pan with cooking spray; dust with flour.
To prepare cake, place the egg substitute, granulated sugar, applesauce, and pumpkin in a large bowl; beat with a mixer at high speed for 1 minute. Add pie spice and cake mix, beating at high speed 2 minutes. Pour batter into prepared pan. Bake at 350° for 35 minutes or until a wooden pick inserted in center comes out clean. Cool cake completely on a wire rack.
To prepare frosting, place the cream cheese and vanilla in a large bowl; beat at medium speed until smooth. Gradually add the powdered sugar, beating just until blended. (Do not overbeat.) Spread frosting evenly over top of cake.