In a food processor, combine the flour, cocoa powder, powdered sugar, and salt. Pulse until everything is evenly combined, about 20 seconds.
Add the cold cubed butter and pulse until the mixture resembles coarse breadcrumbs.
In a small bowl, combine the egg yolk and cold water. Add to the processor and pulse just until small clumps of dough form.
Turn the dough onto your work surface and form into a disc (avoid kneading it). Wrap in plastic wrap and chill for 15 minutes.
Remove the dough from the refrigerator and let it sit at room temperature for a few minutes to soften slightly, making it easier to roll. On a lightly floured surface, roll the dough to a thickness of ⅛ to ¼ inch.
For one 9-inch tart, roll the dough into an 11-inch circle and carefully transfer it to a 9-inch tart pan with a removable bottom. For four 4-inch tarts, cut the rolled dough into 4 portions, each about 1.5 to 2 inches larger than the diameter of your 4-inch tart pans. Then, transfer each piece to an individual pan.
Press the dough gently into the bottom, corners, and sides of the tart pan(s). Roll your rolling pin over the top of the pan to trim excess dough, then push the sides in again to smooth the edges.
Using a fork, prick holes across the bottom of the tart shell(s). Cover with plastic wrap and freeze for 30 minutes until firm. This prevents shrinking during baking.
Preheat oven to 325°F. Line the frozen tart shell(s) with parchment paper and fill with pie weights or dried rice.
Bake for 15 minutes (12-13 minutes for 4-inch tarts). Carefully remove the hot weights and parchment, then bake for an additional 10-15 minutes (8-10 minutes for 4-inch tarts), until the pastry appears matte and feels dry.
Transfer to a wire rack to cool completely.