Preheat oven to 350º. Use 2 - 9" round cake pans that have been lined on the bottom with waxed paper.
In a large bowl, stir together all dry ingredients: flour, cocoa, sugar, baking powder and baking soda.
Add mayonnaise to dry mixture; stirring until well mixed.
Gradually stir in water and vanilla; stirring until batter is smooth.
Pour batter into 2 - 9" round cake pans that have been lined on the bottom with waxed paper.
Bake in 350º oven for 30 minutes or until cake tests done; cool completely before frosting.
In mixing bowl, beat egg; add remaining ingredients; beat well.
Frost cooled cake. Serve