For the pastry (2 tarts):
2 cups all-purpose flour
1/4 cup granulated or superfine sugar
1/2 teaspoon salt
1/2 pound very cold unsalted butter, diced
1/4 cup ice water
For the filling (1 tart):
4 granny smith apples
1/4 teaspoon grated lemon zest
1/4 cup all-purpose flour
1/4 cup granulated sugar
1/4 teaspoon salt
1/4 teaspoon ground cinnamon
1/8 teaspoon ground allspice
4 tablespoons cold unsalted butter (1/2 stick), diced
For the pastry, place the flour, sugar, and salt in the bowl of a food processor fitted with a steel blade. Pulse a few times to combine. Add the butter and toss quickly with your fingers to coat each cube of butter with the flour. Pulse 12 to 15 times, or until the butter is the size of peas. With the motor running, add the 1/4 cup ice water all at once through the feed tube. Keep hitting the pulse button to combine, but stop the machine just before the dough comes together. Turn the dough out onto a well-floured board and form into 2 disks. Wrap with plastic and refrigerate one of the disks for at least an hour. Freeze the rest of the pastry.
Preheat the oven to 450 degrees.
Roll the pastry into an 11-inch circle on a lightly floured surface. Transfer it to a baking sheet lined with parchment paper.
For the filling, peel, core, and quarter the apples. Cut each quarter into 3 chunks. Toss the chunks with the zest. Cover the tart dough with the apple chunks, leaving a 1 1/2-inch border.
Combine the flour, sugar, salt, cinnamon, and allspice in the bowl of a food processor fitted with a steel blade. Add the butter and pulse until the mixture is crumbly. Pour into a bowl and rub it with your fingers until it starts holding together. Sprinkle evenly on the apples. Gently fold the border over the apples, pleating it to make a circle.
Bake the crostata for 20 to 25 minutes, or until the crust is golden and the apples are tender. Let the tart cool for 5 minutes, then use 2 large spatulas to transfer it to a wire rack.