Preheat the oven to 425 F (205 C).
Place a silicone mat on a pizza plate and set aside.
In the mixer bowl, combine the flour, sugar, salt, butter, and shortening.
Mix with the pastry blender until the dough resembles coarse sand.
Add the water and mix until the dough comes together.
Wrap the dough in plastic wrap and refrigerate for 30 minutes.

Roll out the dough into a 13″ (33cm) diameter circle.
Make a mark to define a 9″ (23cm) diameter circle: the location of the fruit.
Spread the apricot jam inside the second circle, then sprinkle with tapioca.

Arrange the fruit on the dough, fitting them together as tightly as possible.
Fold the dough edges towards the center.
Sprinkle the edges with sugar.

Bake for 25 minutes.

Meanwhile, mix all the ingredients for the egg topping.
After 25 minutes of baking, pour the egg mixture over the fruit and continue baking for 15 to 20 minutes.
Remove the tart from the oven and let it cool on a rack for 10 minutes.
Serve warm or at room temperature.