Add the unsalted butter and powdered sugar to the bowl of a stand mixer fitted with the paddle attachment, and mix together on medium-high speed until well combined, approximately 2 minutes.
Add egg yolk and vanilla extract, and continue mixing until combined. Then, add all-purpose flour and Dutch-processed cocoa powder, and mix until just combined. Be sure to scrape the sides of the bowl to avoid any unmixed lumps of butter.
Turn dough out onto a sheet of parchment paper, and place a second sheet of parchment paper on top. Use your hands to press the dough into a disc, and then use a rolling pin to roll out the dough between the parchment sheets until it is approximately 1/8in thick. Place the dough (still between the parchment sheets) onto a half sheet pan, and chill in the fridge for at least 30 minutes until firm.
Once chilled, remove the top sheet of parchment, and cut out 3 discs approximately 6" in diameter (use your 4" tart pans to help you measure). Lift discs off of the bottom sheet of parchment, and gently press into tart pans. Use a sharp knife to trim excess dough along the top of the pans, and then use a fork to dock the dough all over. Place lined tart pans back on a sheet pan and in the fridge for at least 20 minutes until firm.
While the lined tart pans are chilling, heat the oven to 350ºF. Bake the tart shells (can leave on the sheet pan, and no need to weigh down with pie weights!) until slightly darkened around the outsides and fully matte in appearance throughout, approximately 15 minutes. Remove from oven and place on a cooling rack. Once cool, remove from tart pan.