Combine flour, butter, cocoa, and confectioners' sugar in a food processor. Blend until mixture resembles fine crumbs. Add egg and blend briefly to combine into the dough.

Roll out crust dough on a lightly floured work surface using a lightly floured rolling pin. Place in a 8-inch tart pan with removable bottom. Prick pastry dough liberally with a fork. Chill for 1 hour.

While crust dough chills, preheat the oven to 350 degrees F (175 degrees C).

Bake crust in the preheated oven until golden brown, about 15 minutes. Remove from oven and set on a wire rack to cool. Reduce oven temperature to 300 degrees F (150 degrees C).

Melt dark chocolate chips in a double boiler, about 5 minutes; remove from heat.

Beat mascarpone cheese, eggs, and sugar together in a bowl using an electric mixer until smooth. Pour in melted chocolate and orange liqueur; stir to combine. Pour filling into the prepared crust.

Bake in the preheated oven until set, about 40 minutes. Remove from oven and let cool before serving.