The name is derived from the time that eggs, butter and shortening were rationed. Hence the innovation of the mayo. This is from the “America’s Best Lost Recipes” cookbook.
2 cups all-purpose flour
1/4 cup Dutch-processed cocoa powder
1 1/2 teaspoons baking powder
1 teaspoon baking soda
1 cup mayonnaise
1 cup granulated sugar
1 teaspoon vanilla extract
1 cup water
4 tablespoons unsalted butter
1/2 cup packed light brown sugar
2 tablespoons milk
1 cup confectioners’ sugar
1. FOR THE CAKE: Adjust oven rack to the middle position and heat oven to 350 degrees. Grease and flour a 9-inch square baking pan. Whisk flour, cocoa, baking powder, and baking soda in medium bowl.
2. Stir the mayonnaise, granulated sugar, and vanilla together in a large bowl until smooth. Add the water and stir until combined. Whisk in the flour mixture until incorporated. Scrape the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, 30 to 35 minutes. Cool completely in the pan, at least 45 minutes.
3. FOR THE FROSTING: Melt the butter in a small saucepan over medium-high heat. Stir in the brown sugar and bring to a boil. Boil until the mixture begins to thicken, about 2 minutes. Then, off the heat, carefully stir in the milk. Return to a boil, then remove from the heat to cool until just warm, about 30 minutes. Stir in the confectioners’ sugar and spread the icing evenly over the cake. The cake can be stored at room temperature for up to three days.
Here’s the finished product, I ended up having to bake it about 43 minutes before the center was set: