Make the crust: In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, powdered sugar and butter. Mix on medium speed until the mixture forms coarse, crumbly pieces.

Add the egg and vanilla and mix just until the dough comes together. If the dough feels soft, refrigerate for 15 minutes.

Press the dough evenly into a 10- to 11-inch/25- to 28-centimeter tart pan, covering the bottom and sides. Press firmly into the corners to create an even, thin crust.

Trim the excess dough from the edges. Gather the scraps into a ball and freeze. Freeze the tart shell until firm, at least 30 minutes or overnight.

Make the filling: Combine the dark chocolate, white chocolate and butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until melted and smooth. Let cool slightly.

Whisk in the sugar, then whisk in the eggs one at a time. Add the flour and stir just until combined.

Pour the filling into the frozen tart shell. Coarsely grate the frozen pastry scraps over the filling.

Bake until the edges are set and the center is just slightly soft, about 40 minutes.

Let cool completely, then dust with powdered sugar. Serve at room temperature.

Store in an airtight container at room temperature.