In a mixing bowl, whisk together flour, granulated sugar, cocoa powder, and salt until combined. Cut in the butter until the mixture resembles coarse crumbs. Mix in the beaten egg until a dough forms, then chill for 30 minutes.

Preheat your oven to 350°F. Roll out chilled dough to about ¼ inch thick and fit into a 9-inch tart pan. Prick the bottom and bake for 15 minutes.

Heat milk in a saucepan until steaming. Whisk together egg yolks, sugar, and flour in a bowl. Gradually stir in hot milk, then return to saucepan and cook until thickened. Remove from heat and mix in dark chocolate until smooth.

Pour the chocolate filling into the cooled crust and smooth the top. Refrigerate for at least 30 minutes to set.