Coat a 9-inch fluted round tart pan with a removable bottom with cooking spray.

Make the crust: Whisk together flour, cocoa powder, chopped pistachios, and ¼ teaspoon salt.

Beat butter on medium speed until fluffy, about 3 minutes.

Add sugar, and beat until pale, about 2 minutes.

Reduce speed to low, and add vanilla, then flour mixture; beat until just combined and dough holds together when pressed between 2 fingers.

Press dough into a disk, and wrap in plastic. Refrigerate for 15 minutes.

Roll out dough to an 11-inch round, ¼ inch thick on a lightly floured surface.

Press dough into bottom and up sides of tart pan. Trim excess dough flush with edges of pan using a knife.

Refrigerate until firm, at least 1 hour or overnight.

Meanwhile, preheat oven to 325 degrees.

Bake until firm, about 30 minutes. Let cool completely; reduce oven temperature to 300 degrees.

Meanwhile, make the pistachio paste: Pulse pistachios, sugar, and ¼ teaspoon salt in a food processor until mixture begins to clump together.

Add oil, and pulse until smooth and pastelike.

Spread evenly into bottom of cooled tart shell, pressing firmly with the bottom of a measuring cup until flat and smooth.

Make the filling: Place chocolate in a heatproof bowl.

Heat cream and milk in a saucepan over medium heat until almost boiling; pour over chocolate.

Let stand for 2 minutes. Slowly whisk until smooth.

Let cool for 10 minutes. Stir in egg until combined.

Place tart shell on a baking sheet, and pour in filling.

Bake until just set, 30 to 35 minutes. Let cool.

Garnish with finely chopped pistachios.