In the mixer bowl, put the flour, sugar, salt, butter, and shortening.
Mix with the pastry blender until the dough resembles coarse sand.
Incorporate the water and mix until the dough forms.
Wrap the dough in plastic wrap and refrigerate for 30 minutes.

Divide the dough in two and roll out on a floured surface.
Line a buttered tart mold with a sheet of dough and sprinkle with tapioca. Set aside.

In a bowl, mix all the ingredients for the blueberry filling.
Pour into the reserved tart shell.

Cover with the second sheet of dough and press the edges all around.
Make cuts with a knife for ventilation.

Preheat the oven to 425 F (205 C) and place the rack at the bottom of the oven.

Brush the tart with the beaten egg, then bake for 30 minutes.
Reduce the oven to 375 F (190 C) and continue baking for 30 minutes more.
Let cool a bit before serving warm with vanilla ice cream.