Sift the all-purpose flour onto a pastry board. Cube the butter and add it to the flour along with the powdered sugar and salt. Chop all the ingredients with a knife. Add almond flour and egg, and mix to combine into a smooth dough. If it is too dry, add a tablespoon or two of milk. Form into a smooth ball, wrap in plastic, and place in the fridge for about an hour.
Preheat the oven to 390°F and grease small cupcake molds. Lightly dust a work surface with flour and place the dough on it. Roll out the dough to a thickness of ½ inch. Cut out circles slightly larger than the diameter of the prepared molds. Transfer the circles into the molds and use a fork to poke holes in the bottom. Bake for about 12 minutes, until golden brown. Remove from the oven and let cool.
Meanwhile, prepare the filling by whipping the mascarpone cheese with powdered sugar and vanilla. Place the filling in the baked tarts and top with berries. Serve right away.