Put the flour, cocoa, confectioners’ sugar and salt in a food processor and pulse a couple of times to combine. Scatter the pieces of butter over the dry ingredients and pulse until the butter is coarsely cut in — you should have pieces the size of oatmeal flakes and some the size of peas. Stir the yolk, just to break it up, and add it a little at a time, pulsing after each addition.
When the egg is in, process in long pulses — about 10 seconds each — until the dough, which will look granular soon after the egg is added, forms clumps and curds. Just before you reach this stage, the sound of the machine working the dough will change — heads up. Turn the dough out onto a work surface and very lightly and sparingly knead the dough just to incorporate any dry ingredients that might have escaped mixing.
Press the dough into the buttered pan. Freeze for at least 30 minutes, preferably longer, before baking.
To partially or fully bake the crust:
Center a rack in the oven and preheat the oven to 375° Fahrenheit (190° Celsius, Gas Mark 5).
Butter the shiny side of a piece of aluminum foil and fit the foil, buttered side down, tightly against the crust. (Since you froze the crust, you can bake it without weights.) Put the tart pan on a baking sheet and bake the crust for 25 minutes. Carefully remove the foil. If the crust has puffed, press it down gently with the back of a spoon. For a partially baked crust, patch the crust as necessary, then transfer the crust to a cooling rack (keep it in its pan).
To fully bake the crust:
Bake for another 8 minutes or so, or until it is firm and golden brown. Keep a close eye on the crust's progress — it can get too dark in a flash. Transfer the tart pan to a rack and cool the crust to room temperature before filling.