In a mixing bowl, combine the flour, sugar, and salt. Add the cold, cubed butter and use a pastry cutter or your fingers to work it into the flour until the mixture resembles coarse crumbs. Beat the egg with the vanilla extract and add it to the dough. Mix until it begins to come together, adding cold water 1 tablespoon at a time if needed. Divide into two discs, wrap in plastic, and chill for 30 minutes.

In a saucepan, heat the milk over medium-low heat. If using a vanilla bean, split it and add both seeds and pod. Heat until steaming, then remove and let steep for 10 minutes. In a bowl, whisk the egg yolks, sugar, and cornstarch until pale and thick. Gradually whisk in the warm milk (remove the pod if used). Return the mixture to the saucepan and cook over medium heat, stirring constantly until it thickens and boils, about 5–7 minutes. Remove from heat, stir in the butter until smooth, then cover with plastic wrap pressed directly onto the surface. Let cool completely.

Preheat the oven to 350°F (175°C). Lightly grease a 9-inch tart pan with a removable bottom. Roll out one chilled dough disc and press it into the tart pan, trimming any excess. Prick the base with a fork. Spread the cooled custard evenly over the crust. Roll out the second dough disc and place it over the filling. Seal and trim the edges, and cut small slits in the top for ventilation.

Brush the top with beaten egg or milk. Sprinkle the pine nuts evenly across the surface. Bake for 35–40 minutes or until golden brown and the filling is set.

Allow the tart to cool completely in the pan. Dust with powdered sugar just before serving.