Because the cookies are easier to grind when they're brittle, this recipe calls for crisp ones.
Preheat oven to 350 degrees. Make the crust: Stir together cookie crumbs and melted butter. Press into bottom and up sides of a 9 1/2-inch fluted tart pan with a removable bottom. Refrigerate until chilled, about 30 minutes.
Bake until firm and darkened, 10 to 12 minutes. Let cool completely on a baking sheet. Meanwhile, make the filling: Heat cream in a saucepan until just starting to boil. Pour over chocolate in a bowl. Let stand for 1 minute, then stir. Whisk in egg, milk, and butter. Pour into cooled crust.
Reduce oven temperature to 300 degrees. Bake tart until edges of filling are set but center still jiggles slightly, 20 to 24 minutes. Transfer to a wire rack. Serve warm or at room temperature. Top with creme fraiche.
Tart can be refrigerated for up to 1 day.