PREHEAT oven to 350° F. Grease and flour two 8-inch-round baking pans.
COMBINE flour, sugar and cocoa in large mixer bowl. Stir in mayonnaise and vanilla extract; beat for 2 minutes. Combine warm water and baking soda in small bowl. Add to cocoa mixture slowly while beating until well blended. Pour batter into prepared pans.
BAKE for 25 to 30 minutes or until wooden pick inserted in centers come out clean. Cool in pans for 15 minutes; invert onto wire racks to cool completely. Frost with Frosting.
BRING cream, butter and sugar to a simmer in medium, heavy-duty saucepan, stirring until butter melts. Remove from heat. Add morsels; let sit for 2 minutes. Whisk until smooth. Whisk in vanilla extract. Pour into medium bowl. Refrigerate for about 1 1/2 hours, stirring occasionally, until frosting is thick enough to spread.