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Combine the flour, cocoa powder, sugar, and salt in the bowl of a food processor. Pulse to combine.
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Sprinkle the butter pieces over the flour mixture. Pulse the mixture until it resembles a coarse meal with a few pea-sized pieces of butter.
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In a separate bowl, whisk together the egg yolk, vinegar, and ice water. Drizzle the liquid mixture over the flour mixture and pulse just until the dough comes together.
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Transfer the dough to a lightly floured surface and shape it into a 1-inch thick disk. Wrap the dough in plastic wrap and chill in the refrigerator for one hour.
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Preheat the oven to 350 F.
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Place the dough on a lightly floured surface and roll out to a 14-inch round. Transfer the dough to a 9-inch pie dish.
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Trim the crust, leaving about a 1-inch overhang. Fold the overhang under and use your thumb and forefinger to crimp the edge. Chill the pie crust in the freezer for 15 minutes.
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Line the pie crust with parchment paper and fill it with pie weights or dried beans. Bake the crust until it is dry around the edges, about 20 minutes. Remove the parchment paper and pie weights and bake an additional 3-5 minutes, until the surface of the crust is dry and set.
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Let the pie crust cool slightly while you make the pie filling. Adjust the oven temperature to 425 F.