Position a rack in the center of the oven and preheat to 350F.
Starting on low speed and gradually increasing to medium, cream the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment. Add the eggs, one at a time, paddling until absorbed into the mixture. Add the zest, and then add the water in a thin stream, letting it run down the side of the bowl.
Stop the motor and lower the bowl. Put the pastry flour, all-purpose flour, salt, and baking powder in a sifter and sift into the bowl. Starting on low speed and gradually increasing to medium, mix until the dough comes together.
Dust your work surface with flour and roll out the dough to a thickness of 1/8 inch. Fit the dough to a 9-inch fluted tart pan. Dock it all over with the tines of a fork.
Bake until dough is lightly golden brown on top and bottom, 15 to 20 minutes. Remove the pan from the oven and let the tart shell cool completely.
In a mixing bowl, fold together the cream custard and whipped cream to make French cream.
Use a rubber spatula to transfer the French cream to the tart, smoothing the top. Artfully arrange the berries on top. Dust with powdered sugar and serve.
The frutti di bosco should be served right away, but can be refrigerated, covered loosely with plastic wrap, for up to 1 day.