Preheat oven to 350 degrees. Make the cake: Butter and flour a 7-inch round cake pan (3 inches deep). Sift flour, cocoa powder, granulated sugar, baking soda, baking powder, and 3/4 teaspoon salt into a large bowl.
Add eggs, warm water, buttermilk, oil, and vanilla. Beat with a mixer on medium-high speed until smooth, about 3 minutes.