Preheat oven to 350°F. Grease two 8- or 9-inch round cake pans or spray with nonstick baking spray. Line the bottoms of the pans with rounds of parchment paper, grease the parchment, then flour the insides of the pans, tapping out excess. Set pans aside.
In the bowl of an electric mixer, sift together the flour, sugar, cocoa powder, baking soda, baking powder and salt.
In a medium bowl, whisk together the eggs, buttermilk, coffee, oil and vanilla.
2 eggs, 1 cup buttermilk, 1 cup hot coffee, ½ cup vegetable oil, 1 tablespoon vanilla extract
Add the wet ingredients to the dry ingredients. Mix on lowest speed or by hand to moisten the dry ingredients, then turn the mixer up to medium for 2 minutes. Scrape the sides and bottom of the bowl and mix for an additional 20 seconds The batter will be very thin.
Divide the batter evenly between the prepared cake pans.
Bake for 20 minutes and rotate the pans in the oven. Continue to bake until a toothpick inserted into the center of one of the cakes comes out almost clean just with a few moist crumbs, about 12 more minutes. Cakes baked in 8-inch pans will take longer than those baked in 9-inch pans.
Cool the cakes in the pans on wire racks for 20 minutes, then carefully turn them out onto cooling racks to cool completely.