Heat oven to 350°F. Grease and flour 15x10x1-inch jelly-roll pan. Set aside.
Stir together flour, baking powder and salt in large bowl. Set aside.
Beat 1 1/2 cups sugar and 3/4 cup butter in large bowl at medium speed, scraping bowl occasionally, until creamy. Add 1 egg at a time, beating well after each addition. Add vanilla. Reduce speed to low. Add flour mixture alternately with milk, beating well after each addition just until mixed.
Place 1 1/2 cups batter into small bowl. Add remaining 1/4 cup sugar, 1/4 cup cocoa and water; stir until well mixed.
Spoon 3/4 of plain batter into bottom of prepared pan. Spoon chocolate batter over plain batter. Spoon remaining plain batter on top, allowing some of chocolate batter to show through. Swirl batters together gently with knife or spatula for marbled effect.
Bake 22-27 minutes or until toothpick inserted in center comes out clean. Remove from oven. Cool completely.
Beat 1/2 cup butter in medium bowl at medium speed until creamy. Gradually beat in powdered sugar, 2/3 cup cocoa, 2 tablespoons milk and vanilla. Continue beating, adding enough milk for desired spreading consistency. Frost cooled cake.
Unsweetened cocoa is used in both the cake and the frosting. Unsweetened cocoa powder is made by removing most of the fat from chocolate, then drying it and grinding it into a powder. Dutch-process cocoa has been treated to neutralize its acidity and should not be used unless a recipe specifically calls for that type of cocoa. Do not substitute instant cocoa mix for unsweetened cocoa powder, as it has been blended with dried milk and sugar.