Preheat oven to 350 degrees. Spray two 9-by-13-inch baking pans with cooking spray. Line with parchment, leaving an overhang on long sides. Spray parchment. Flour pans, tapping out excess.
Sift together cocoa powder, flour, sugar, baking soda, baking powder, and salt in a large bowl. Mix in eggs, buttermilk, water, oil, and vanilla until smooth. Divide batter between pans. Bake, rotating halfway through, until tops of cakes spring back when pressed and a toothpick comes out clean, about 35 minutes. Let cool completely, then lift cakes from pans using parchment. Remove parchment.