In a small mixing bowl, beat the eggs, buttermilk, and vanilla extract together. Add this to the cake batter and mix well until smooth.
Pour the batter into the prepared baking sheet pan. Bake for 20-25 minutes, or until a toothpick inserted in the center of the cake comes out clean.
While the cake is baking, prepare the icing. In a saucepan, melt the butter, cocoa powder, milk, and vanilla extract together over medium heat. Once melted and smooth, remove from heat and stir in the powdered sugar until the icing is well mixed and free of lumps.
Once the cake has finished baking, remove it from the oven and immediately pour the icing over the hot cake, spreading it evenly.
Allow the cake to cool completely before cutting and serving.
