To prepare cake: Preheat oven to 350 degrees. Grease and flour 2 (8-inch) cake pans and line bottoms with parchment paper. In a small bowl, combine coffee and cocoa, stirring to dissolve cocoa. Cool to room temperature and reserve. In bowl of an electric mixer on medium speed, cream together shortening and sugar for 2 minutes. Add eggs, one at a time, beating well after each addition. Increase speed to high and beat until light and fluffy, 3 to 5 minutes. In a medium bowl, stir together cake flour, baking powder, baking soda and salt until combined. Reduce mixer speed to low and gradually add flour mixture to batter in thirds, alternating with coffee-cocoa mixture. Mix until thoroughly combined. Pour into prepared cake pans and bake 40 to 45 minutes, or until top springs back when lightly touched. Remove from oven to a wire rack, cool completely, remove from pans to flat plates, cover in plastic wrap and freeze overnight.
To prepare frosting: In a small saucepan over low heat, combine flour and milk into a smooth paste and cook, stirring constantly, until it thickens, approximately 10 to 15 minutes. Remove from heat, cover surface with waxed paper to prevent a skin from forming and cool to room temperature. In bowl of an electric mixer fitted with a whip attachment on low speed, cream together granulated sugar, butter and shortening. Increase speed to high and beat for 5 minutes. Gradually add small spoonfuls of cooled milk mixture, beating well after each addition, working slowly so paste mixture is beaten in thoroughly. Reduce speed to low and gradually add vanilla and powdered sugar.
To assemble cake: Remove cake from freezer. If cake is domed, slice off dome (save it for a snack) and slice each layer in half horizontally to make two layers (you now have four layers). Put bottom layer on a cake plate, top with 3/4 cup frosting, and repeat with each filled layer. Cover top and sides of layered cake with a thin layer of frosting to seal in crumbs, then cover top and sides of cake with remaining frosting. Sprinkle top and sides with coconut and serve.