Preheat oven to 350°F. Spray three 6-inch round baking pans with vegetable pan spray.
In medium bowl, combine flour, baking powder and salt. In small microwave-safe bowl, heat milk until hot. Add white chocolate; stir until chocolate melts and mixture is smooth. Add vanilla; set aside. In large bowl, cream butter and sugar with electric mixer until light and fluffy. Add eggs, one at a time, mixing well. Add flour mixture alternately with melted chocolate mixture, mixing until just combined. Gently fold in grated chocolate; divide batter between the two pans.
Bake 28 to 32 minutes or until toothpick inserted into center comes out clean. Cool 10 minutes in pan; remove and cool completely on cooling grid.
Meanwhile prepare icing. In large bowl, beat butter with electric mixer until light and fluffy. Add cocoa, milk and vanilla; mix well. Gradually add sugar, one cup at a time, beating well on medium speed. Continue beating at high speed until light and fluffy.
Stack cooled cake layers on serving plate, spreading icing between layers. Spatula ice cake.
Makes 12 - 16 servings.