Preheat oven to 350ºF. Grease and lightly flour two 9” round cake pans.
In a large bowl, beat eggs, sugar and vanilla with an electric mixer on medium, until light and fluffy. Add flour, water, mayonnaise, unsweetened cocoa, baking soda and baking powder, blend well. Pour batter in prepared pans. Bake for 30-35 minutes or until a pick inserted n center comes out clean. Cool 10 minutes; remove from pans, Cool completely on wire racks.
Frosting: Beat butter and vanilla. Add confectioners sugar and cocoa alternately with milk, beating well after each addition.
Set first layer top side down on a platter, spread 1/3 of frosting on cake, top with other layer top side up and frost sides and top with remaining frosting.
**Cake may be baked in a 9x13” baking pan for 30-35 minutes or until a toothpick inserted in center comes out clean. Cool on wire rack. Frost cake while still in pan.