Step 1

Heat the oven to 375°F with a rack in the middle position. In a medium bowl, whisk together the 195 grams (1½ cups) flour and ¼ teaspoon salt, then make a well in the center; set aside.

Step 2

In a small saucepan, combine the butter, shortening and ¼ cup water. Bring to a simmer over medium-high, stirring to melt the solids. As soon as they’re melted and the mixture is simmering, pour it into the well of the dry ingredients. Working quickly, stir with a silicone spatula until the dry ingredients are evenly moistened and without any dry patches; the dough will be very soft and resemble wet mashed potatoes. Turn it out onto a large sheet of plastic wrap and, using your hands, form it into a 6- to 8-inch disk.

Step 3

Cover the dough disk with another large sheet of plastic wrap and roll it into a 12-inch round of even thickness. Peel off the top sheet of plastic. Using the bottom sheet, carefully flip the round into a 9-inch pie plate, centering it as best you can. Ease the dough, still on the plastic, into the corners and up the sides of the pie plate. Carefully peel off the plastic. If needed, patch any tears in the dough. Trim the excess dough and flute or crimp the edge. Carefully line the dough with a large sheet of foil, gently pressing it into the corners and up the sides, then fill with about 2 cups pie weights.

Step 4

Bake until the dough is set, about 20 minutes. Carefully lift out the foil with weights, then prick the pie shell all over with a fork to deflate any air bubbles and prevent additional ones from forming. Bake until the shell is lightly browned, another 12 to 15 minutes. Transfer to a wire rack and let cool. Reduce the oven to 350°F.

Step 5

In a large bowl, whisk together the sugar, cocoa, cornstarch, the remaining 33 grams (¼ cup) flour and the remaining ¾ teaspoon salt. Whisk in the egg yolks and milk. Pour the mixture into a large saucepan.

Step 6

Have ready a fine-mesh sieve set over a medium bowl. Set the saucepan over medium and bring the mixture to a gentle simmer, whisking constantly (do not allow it to reach a vigorous simmer); it will thicken to the consistency of sour cream. Immediately scrape the mixture into the sieve and work it through with a silicone spatula; be sure to scrape the bottom of the sieve to collect the filling that clings. Whisk in the vanilla.

Step 7

Pour the filling into the pie crust, then carefully tilt the pie so the filling settles in an even layer. Bake until the filling jiggles slightly when the pie is gently shaken, 30 to 35 minutes.

Step 8

Cool completely on a wire rack. Serve at room temperature or refrigerate for about 2 hours (cover if refrigerating longer) and serve chilled.