Preheat oven to 300°F and grease a 13x9 inch baking pan on the bottom and sides.
In a large bowl, whisk together flour, sugar, cocoa powder, salt, baking powder, and baking soda.
Using an electric mixer, beat the eggs until bright yellow and slightly thick.
Add vegetable oil, brewed coffee, and vanilla extract to the eggs, mixing until well combined.
Alternately add the dry flour mixture and buttermilk to the wet ingredients, starting and ending with flour, mixing until just incorporated.
Pour batter into the prepared pan and drop it from a few inches above the counter to remove air bubbles.
Bake at 300°F for 1 hour, or until a toothpick inserted in the center comes out clean.
For the frosting, beat softened butter and peanut butter in a medium bowl until smooth with an electric mixer.
Gradually add confectioners' sugar while mixing, then add milk one tablespoon at a time until frosting reaches thick, spreadable consistency.
Beat frosting for at least 3 minutes until fluffy.
Spread frosting evenly over the cooled cake.