Step 1

FOR THE TART SHELL: Whisk together egg and vanilla in 1-cup liquid measuring cup; set aside. Pulse flour, sugar, and salt in food processor until combined, 2 pulses. Scatter butter over flour mixture; process until mixture looks like very fine crumbs with no pieces of butter visible, about 20 seconds. With processor running, add egg mixture and continue to process until dough just forms mass, about 18 seconds longer.

Step 2

Transfer dough to center of 18 by 12-inch piece of parchment paper. Place second sheet of parchment on top of dough and press with your hand to ½-inch thickness. Using rolling pin, roll out dough so it nearly reaches edges of parchment. Using your flat hand on parchment, smooth out wrinkles on both sides. Transfer dough with parchment to baking sheet and freeze until firm, about 30 minutes.

Step 3

Place dough and parchment on counter and peel away top layer of parchment. Replace top layer of parchment, flip dough and parchment, and peel away second piece of parchment. Invert 9-inch metal tart ring on left half of dough and press to cut out circle (leave circle on parchment). Using paring knife and ruler, cut right half of dough lengthwise into 1-inch-wide strips. Place removable bottom in tart pan. Lift dough round (if necessary, use thin spatula to loosen) and fit into bottom of tart pan, pressing edges of dough firmly into corners (it's OK if some dough smears up sides of tart pan). Lift strips and fit into sides of pan, overlapping strips only slightly. Trim final strip to fit. (Dough scraps can be sprinkled with sugar and baked as cook's treat.) If at any point dough becomes too soft to manipulate, freeze for 15 minutes.

Step 4

Freeze tart shell until very firm, about 20 minutes. While tart shell chills, adjust oven rack to middle position and heat oven to 350 degrees.

Step 5

Hold paring knife parallel to counter and shave off any excess dough to force dough into flutes for clean edge. Spray large sheet of heavy-duty aluminum foil with vegetable oil spray. Place foil sprayed side down in tart shell and smooth gently along bottom and sides. Fill with pie weights. Bake on rimmed baking sheet until tart shell is golden and set, about 30 minutes, rotating sheet halfway through baking. Remove foil and weights and continue to bake tart shell until fully baked and golden brown, about 10 minutes longer. Transfer sheet to wire rack and let cool completely, about 30 minutes.

Step 6

FOR THE FILLING: Place fine-mesh strainer over medium bowl. Whisk half-and-half; egg yolks; cocoa, if using; and salt in small saucepan until combined. Cook mixture over medium-low heat, stirring constantly and scraping bottom of saucepan with heatproof spatula, until mixture is thickened and silky and registers 170 to 175 degrees, 5 to 7 minutes. Remove from heat. Working quickly, whisk in chocolate and vanilla until smooth. Add melted butter and whisk gently until incorporated. Pour mixture into prepared strainer and transfer strained mixture to cooled tart shell. Let cool completely, about 20 minutes, and then refrigerate until filling is set, at least 2 hours or up to 24 hours.

Step 7

Remove outer ring from tart pan. Insert thin metal spatula between crust and pan bottom to loosen tart; slide tart onto serving platter. Cut into wedges and serve. (Leftovers can be wrapped loosely and refrigerated for up to 3 days.)