Step 1Heat the oven to 400 degrees.
Step 2In the bowl of an electric mixer or food processor, combine the all-purpose flour, cake flour, sugar and salt. Distribute the butter over the top and mix until the butter is thoroughly incorporated and the mixture resembles moist cornmeal.
Step 3Combine the ice water and vanilla and sprinkle over the top of the dough. Mix until the dough comes together and pulls cleanly away from the sides of the bowl.
Step 4Remove the dough from the bowl and flatten it into a disk, then wrap it in plastic wrap and refrigerate until ready to use.
Step 1In a medium bowl, toss together the berries, sugar and cornstarch and stir gently until they are well-coated. Set aside.
Step 2On a lightly floured surface, roll the crostata dough out to a roughly 16-inch-diameter circle. Leave it a little thick; the added texture is better. Transfer the dough to a cookie sheet, then place the sweetened fruit mixture in the center and distribute it in a low mound, leaving a 2-inch border.
Step 3Fold the edges of the dough over the fruit to form a 6-sided tart, with the fruit showing in the center: Fold one edge over, then fold the second edge over, pleating the dough as necessary and pressing firmly on the pleat.
Step 4Lightly brush the surface of the dough with a little water and sprinkle with coarse sugar. Bake until the crust is brown and the fruit is soft and thickened, 30 to 35 minutes. Rotate the crostata halfway through baking for even coloring.
Step 5Remove the crostata from the oven and cool 10 minutes before cutting and serving with vanilla ice cream.