Place all-purpose flour (potato starch, tapioca flour, and rice flour for gluten free crust) and hazelnut meal in a food processor. Pulse a few times to combine. Add powdered sugar and butter. Pulse again until mixture resembles coarse bread crumbs. Add cold water and pulse again until a sticky dough forms.
Turn dough onto a lightly floured surface. Knead lightly or pat to form a disk. Wrap and chill in the refrigerator for 30 minutes.
Preheat oven to 375°F (190°C).
Remove dough from refrigerator. Unwrap onto a non-stick pastry mat (or a large piece of wax paper). Roll into a 12-inch circle. Invert onto a 9-inch removable bottom tart pan. Press the dough evenly onto the bottom and sides of the tart pan. Trim dough to the edges of the pan, patching where necessary.
Prick sides and bottom of crust with a fork. Line crust with double layer of foil and bake for 15 minutes.
Form trimmed edges into a ball. Roll it out and cut into desired shapes with a small cookie cutter. (This step is optional.)
Combine blueberries, strawberries, and raspberries in a large bowl. Add granulated sugar and all-purpose flour (or rice flour for gluten free option). Mix well. Add lemon zest and lemon juice.
Remove tart crust out of the oven and reduce oven temperature to 350°F (180°C). Spoon filling into tart crust. Place cut-out dough decoratively all over the filling.
Return the tart to the oven and bake for another 45 minutes. Remove and allow tart to cool before serving with freshly whipped cream.