• Preheat oven to 350°F. Grease and flour a 9-by-13-by-2-inch baking pan.
  Butter and flour for the baking pan
• In a large mixing bowl, combine the flour, granulated sugar, and salt; whisk or stir to blend thoroughly. Set aside.
  2 cups all-purpose flour | 2 cups granulated sugar | 1/2 tsp salt
• 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 extract. Beat with an electric mixer until smooth.
  1/2 cup butter | 1/2 cup shortening | 1/4 cup unsweetened cocoa powder | 1 cup water | 1/2 cup buttermilk | 1 tsp baking soda | 2 eggs | 1 tsp vanilla extract
• Spoon the batter into the prepared baking pan and spread evenly.
• Bake in the preheated oven for 40 to 45 minutes, or until the cake springs back when lightly touched with a finger. The cake is frosted while hot, so make the frosting just before the cake is done.

Frosting

The cake is frosted while hot, so start the frosting during the last few minutes of baking.
• Combine 1/2 cup of butter, 1/4 cup of unsweetened cocoa powder, and milk in a medium saucepan. Bring the mixture just to a boil over medium-high heat; remove from the heat.
  1/2 cup butter, softened | 1/4 cup unsweetened cocoa powder | 6 tbsp milk
• Add confectioners' sugar and vanilla extract to the saucepan and stir vigorously with a wooden spoon until smooth. Stir in coconut and pecans.
  1 pound confectioners' sugar | 1 tsp vanilla extract | 2 cups sweetened flaked coconut | 1 cup chopped pecans
• Spread the frosting on the hot cake as soon as it comes out of the oven. Cool the frosted cake on a rack, then slice and enjoy.
Spread the frosting quickly over the hot cake—it thickens as it cools.