In a large bowl, combine flour, cocoa, sugar, baking powder, baking soda, and salt. Whisk until combined. Using a fork, pastry blender or your hands, add butter pieces to the flour and mix until coarse little crumbles remain.
Add buttermilk and vanilla. Stir until just combined. Don't overmix.
Press dough together with your hands on a sheet of parchment paper or pastry board. Use a knife to cut squares or a biscuit cutter to shape the dough into rounds.
Bake for 20 to 25 minutes, or until biscuits are set and slightly golden on the edges. Serve immediately.