What to do when you want a nice dessert and you don't have any eggs on hand, and you're too lazy to go to the store? Back during the Depression (before my time!) eggs were sometimes scarce or expensive so many recipes were adapted to be egg-free. This cake is one of them. The frosting is my mother's.
FOR CAKE: In a large mixing bowl, combine flour, sugar, salt, soda, and cocoa. Make 3 wells. Pour oil into one well, vinegar into second, and vanilla into third well.
Pour cold water and cold coffee over all, and stir until well combined.
Bake in a greased 9x13" baking pan in a preheated 350-degree oven for 30 to 40 minutes, or until toothpick inserted near center comes out clean. Cool completely before frosting.
FOR FROSTING: mix the brown sugar with 2 Tbsp. milk in a medium saucepan. Over low heat bring to a ROLLING boil. Remove from heat. Add the butter, vanilla, and powdered sugar. Beat until cool and then frost the cake. If frosting is too thick, you can add a little more milk.