Pulse the flour, cocoa powder, powdered sugar, and salt in a food processor until combined. Scatter the cold, cubed butter over the dry ingredients. Pulse about 10 - 15 times, scraping the bowl as necessary, until the mixture is crumbly.
Add the egg and vanilla and pulse 10 - 15 times, or until the mixture is moist and crumbly.
Turn the dough out onto a lightly floured surface and form a ball. Flatten the ball into a disc about 6 inches wide. Wrap in cling film and chill in the fridge for an hour.
Take the dough out and let it soften for just a few minutes. On a lightly floured surface, roll the pastry dough into a 12 inch circle (or larger if you want a thinner crust). Remember to flour both sides of the dough and continually lift it, flip it over, and move the dough around to prevent sticking.
Drape the rolled out dough over your rolling pin and transfer to a 9 inch tart pan. Gently lift and press the dough into the corners of the dish. Trim off the excess. Cover with plastic wrap and place in the freezer for 30 minutes.
Preheat the oven to 375°F and place the tart shell in the freezer for 20 minutes. When the tart dough is firm, take it out of the freezer and prick the bottom a few times with a fork. Crumple up some parchment paper, then unroll it and cover the dough. Cover with pie weights and make sure they are evenly dispersed.
Bake for 20 minutes. Then remove the weights and parchment paper and bake for an additional 5 minutes for a partially baked crust. (If you want a fully baked crust for a different recipe, bake for 10 minutes.)
Set the tart aside to cool slightly.