Make cake: Preheat oven to 350°F. Grease and flour a 9-by-13-inch cake pan. Whisk flour, sugar, baking soda and salt. In a separate bowl, whisk eggs, buttermilk and vanilla.
In a pan, combine butter, cocoa and cola; cook over low heat, stirring, until butter has melted. Stir into flour mixture, then whisk in egg mixture.
Pour batter into cake pan and bake until a toothpick inserted in center comes out clean, 35 to 45 minutes.
Make frosting: Cook butter, cocoa and cola over medium-low heat, stirring, until butter has melted and ingredients are well mixed. Place confectioners' sugar in a large bowl. Pour cola mixture over sugar and whisk well. Stir in vanilla.
Poke holes all over top of hot cake with a fork or toothpick. Pour warm frosting over cake. Let cake cool in pan on a wire rack.