Preheat your oven to 350°F. Grease and flour a 9x13 inch baking pan.
In a large bowl, whisk together flour, sugar, cocoa powder, baking soda, baking powder, and salt.
In a separate bowl, beat eggs until they lighten in color.
Mix in oil, cooled coffee, and vanilla extract into the beaten eggs until well combined.
Gradually add the dry ingredients to the wet mixture, alternating with buttermilk, starting and ending with the flour mixture. Stir until just combined.
Pour the batter into the prepared baking pan, smoothing the top with a spatula.
Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool completely in the pan on a wire rack.
For the frosting, beat together softened butter and peanut butter until smooth.
Gradually add powdered sugar, then beat in milk a tablespoon at a time until the frosting reaches a spreadable consistency.
Frost the cooled cake with the peanut butter frosting and serve.