Sift together flour and sugar into a bowl. Heat butter, cocoa, and Coca-Cola to a boiling point; pour over flour mixture and mix well. Add buttermilk, eggs, and vanilla. Mix well. Pour batter into a greased 13-x-9-inch pan; bake at 350° for 35 minutes. Cool 15 minutes.
Icing:
1 stick butter, softened
3 tablespoons cocoa
1/2 cup Coca-Cola
4 cups powdered sugar
Put butter, cocoa, and Coca-Cola in a saucepan; boil. When butter is melted, remove from heat; add sugar. Mix well and spread on cooled cake. If needed, add a few drops of Coke to make icing more spreadable.
The cook says: My mother always made this cake for me on my birthday when I was small. Even today, at 91 years old, she still bakes me one.