In a food processor, combine the flour, cocoa powder, sugar, and salt. Pulse to blend the dry ingredients.
Add the cold butter and pulse until the mixture forms coarse crumbs, about the size of peas.
Add 4 tablespoons of ice water and pulse. Add more water, one tablespoon at a time, just until the dough starts to clump together. Do not let it form into a full ball. It should hold together when pressed between your fingers.
Turn the dough out onto a surface, shape into a disk, and wrap in plastic wrap. Chill for at least 1 hour or overnight.