How to Make It
Sift together the flour, cocoa powder, yeast, sugar, and salt in a medium bowl. (I do this by setting a fine-mesh sieve into the bowl.)
In another small bowl, or directly in a measuring cup, stir together the water, buttermilk, and melted butter. Pour this over the dry ingredients and mix together with your hands, kneading gently about 2 to 3 minutes until it comes together as a soft, moist ball of dough. Thoroughly coat the dough with a bit of vegetable oil, cover, and place in a warm spot (like the oven with the oven light on) for about an hour, until the dough seems to have expanded slightly and appears almost spongy. Gently punch the air out of it, shape it back into a ball, and refrigerate for at least 2 to 3 hours and up to overnight.
When you’re ready to fry, heat an inch of oil in a medium-sized, heavy-bottomed pot over medium-low heat until it reaches 360° F. (If you don’t have a thermometer, stick the handle of a wooden spoon or chopstick into the oil; if lots of small bubbles dance around it, the oil is ready.) Set a wire cooling rack inside a sheet tray and line the rack with a paper towel.
Meanwhile, use your hands to shape the dough into a 12-by-6-or-so-inch rectangle, about ¼ inch thick, on a lightly floured surface. Cut into 2-inch squares for small beignets or 3-inch squares for large beignets.
When the oil reaches temperature, drop a third of the beignets in and fry for about a minute, then use metal tongs or a slotted metal spoon to flip them over; cook for about a minute on the second side. Remove the finished ones to the towel-lined cooling rack and let the oil return to 360° F before frying the next batch.
Let the beignets cool just slightly, then dust them generously on both sides with powdered sugar (I use a small mesh tea strainer for this). Serve immediately.