For the cake: Heat oven to 350 degrees. Grease two 9-inch round cake pans with baking spray. Line bottom of pans with waxed paper; spray paper with baking spray. Dust with flour; tap out excess.
In a medium bowl, combine flour, cocoa powder, grated chocolate, baking powder, and salt.
In a 2-cup glass measuring cup, stir together buttermilk, food coloring, vinegar, vanilla, and baking soda.
In a large bowl with an electric mixer, beat butter and sugar on medium-high until light and fluffy. Beat in eggs, one at a time, until well blended. Beat in flour mixture alternately with buttermilk mixture on medium-low speed. Pour batter into prepared pans. Bake 25 to 30 minutes or until cake tester inserted in center comes out clean. Cool in pans on a wire rack 10 minutes. Invert onto wire rack; invert again and let cool completely on rack.
For the frosting: Place white chocolate and cream in a small micro-wave-safe bowl. Microwave on high 15 to 30 seconds; whisk until smooth. Let stand 2 minutes; cover with plastic wrap and chill.
In a large bowl with an electric mixer, beat cream cheese, butter and vanilla on medium-high speed until light and fluffy, about 2 minutes. Beat in cooled white-chocolate mixture until blended. On low speed, add confectioners' sugar in batches and beat until combined. Increase speed to medium-high and beat until fluffy, about 1 minute.
To assemble the cake: Cut each cake layer horizontally with a long serrated knife, to make 4 layers. Place one layer on a serving plate and spread with about 1 cup of frosting. Repeat with remaining 3 layers, frosting the top and sides of the cake. Sprinkle coconut on top and sides of cake. Refrigerate cake about 1 hour to let it set.