PREHEAT oven to 350°F. Grease and flour 2 (9-inch) round cake pans. Line bottoms of pans with wax paper.
BEAT eggs, granulated sugar and 1 tsp. of the vanilla in large bowl with electric mixer on medium speed until light and fluffy. Add flour, water, dressing, 2/3 cup cocoa, the baking soda and baking powder; beat until well blended. Pour evenly into prepared pans.
BAKE 30 to 35 min. or until toothpick inserted in centers comes out clean. Cool 10 min.; remove from pans. Immediately remove wax paper. Cool completely on wire racks.
BEAT butter and remaining 1 tsp. vanilla in large bowl with electric mixer on medium speed until creamy. Add combined powdered sugar and 3/4 cup cocoa alternately with the milk, beating well after each addition. Use to fill and frost the cake layers.