Pulse cocoa powder, sugar, salt, and 1¼ cups flour in a food processor to combine. Add butter; pulse until mixture resembles coarse meal. Beat egg yolk and 3 Tbsp. ice water in a small bowl; add to flour mixture and pulse until dough just comes together. Form into a ¾”-thick disk, wrap tightly in plastic, and chill until firm, at least 2 hours.
Preheat oven to 350°. Roll out dough on a lightly floured surface to a 12” round. Transfer to tart pan; lift up edges and let dough slump down into pan, then gently press into edge of pan. Trim dough, leaving about a 1” overhang. Fold in overhang; press to adhere. Prick bottom with a fork. Chill in freezer 15 minutes
Line pie with parchment paper or heavy-duty foil, leaving a 1½” overhang. Fill with pie weights or dried beans. Place on a rimmed baking sheet and bake until crust is dry around the edges, about 30 minutes. Remove parchment and weights and bake until crust is firm and looks dry all over, 5–10 minutes longer. Transfer pan to a wire rack and let crust cool.