Preheat oven to 350°.
Coat 2 (8-inch) round cake pans with cooking spray. Line bottom of each pan with wax paper.
Combine cocoa, water, and butter, stirring with a whisk until blended. Cool.
Combine sugars in a large bowl, stirring well until blended. Add egg substitute; beat 2 minutes or until light and creamy. Add cocoa mixture, and beat for 1 minute.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt. Gradually add flour mixture to bowl; beat for 1 minute or until blended. Stir in vanilla. Pour batter into prepared pans. Bake at 350° for 28 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on a wire rack. Remove from pans. Wrap in plastic wrap, and freeze for 2 hours or until slightly frozen.
Spread ice cream in an 8-inch round cake pan lined with plastic wrap. Cover and freeze 4 hours or until firm.
To assemble cake, place one cake layer, bottom side up, on a cake pedestal. Remove ice cream layer from freezer; remove plastic wrap. Place ice cream layer, bottom side up, on top of cake layer. Top with remaining cake layer.
Combine whipped topping and peppermint extract, and stir until blended. Spread frosting over top and sides of cake. Sprinkle with crushed peppermints. Freeze until ready to serve. Let cake stand at room temperature 10 minutes before slicing.