Preheat oven to 350°.
To prepare cake, combine 1/2 cup cocoa and water in a small bowl; cool. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, and salt, stirring well with a whisk. Place granulated sugar, shortening, and 2 teaspoons vanilla in a large bowl; beat with a mixer at medium speed until well blended. Add eggs, 1 at a time, beating well after each addition. Beat in cocoa mixture. Add flour mixture and buttermilk alternately to sugar mixture, beginning and ending with flour mixture and beating well after each addition.
Pour batter into a 13 x 9-inch baking pan coated with cooking spray. Bake at 350° 30 minutes or until the cake springs back when lightly touched. Cool in pan 10 minutes on a wire rack.
To prepare icing, combine the powdered sugar and 3 tablespoons cocoa in a medium bowl, stirring well with a whisk. Add milk, butter, and 1/2 teaspoon vanilla; stir with a whisk until smooth. Spread icing over cake.