1. Preheat oven to 350 F.
2. Grease and flour a 9-by-13-by-2-inch baking pan.
3. In a large mixing bowl or bowl of a stand mixer, combine the flour, granulated sugar, and salt; whisk or stir to blend thoroughly. Set aside.
4. In a small saucepan, combine 1/2 cup butter, the shortening, 1/4 cup of cocoa, and 1 cup of water; bring to a boil over high heat. Pour the mixture over the flour mixture. Add the buttermilk, baking soda, eggs, and vanilla. Beat with an electric mixer until smooth. Spoon the batter into the prepared baking pan and spread evenly.
5. Bake in the preheated oven for 40 to 45 minutes, or until the cake springs back when lightly touched with finger. The cake is frosted while hot, so make the frosting just before the cake is done.

Frosting

1. Combine 1/2 cup of butter, cocoa, and milk in a medium saucepan. Bring mixture just to a boil over medium-high heat; remove from heat.
2. Add confectioners’ sugar and vanilla to the saucepan and beat with a wooden spoon until smooth. Stir in coconut and pecans.
3. Spread over hot cake right out of the oven. Cool frosted coconut chocolate cake in pan on a rack.