1 Make the dough: In a food processor, pulse the flour, sugar, salt, and butter pieces until the butter is incorporated into small, pea-size pieces.
Open the lid, add 3 tablespoons of the ice water, and pulse again until the mixture looks uniform.
Press a small amount of dough together in your hand. It should hold together firmly. If it feels dry or crumbly and doesn’t hold together well, add more ice water, 1 tablespoon at a time.
2 Refrigerate the dough: Turn the dough out onto the countertop, and press into a flat disk. Wrap in plastic wrap and refrigerate for at least 30 minutes or up to 2 days.
3 Soak the cranberries: In a microwave-safe bowl, heat the cranberries and cranberry juice for 30 to 45 seconds, or until warm. Let the cranberries soak for 15 minutes while you prepare the filling.
Drain and set aside 1 rounded tablespoon of cranberries for garnish.
4 Prepare the apples: Peel, core, and cut the apples into quarters. Cut each quarter into 4 to 5 wedges and place in large mixing bowl. Fold in the cranberries.
In a small bowl, whisk together the flour, brown sugar, cinnamon, and salt. Fold the sugar mixture into the apples and set aside.
5 Preheat the oven to 400ºF. Line a rimmed baking sheet with parchment paper.
6 Roll out the dough: On a floured work surface, roll the dough into a 13-inch circle. Place circle on prepared baking sheet.
7 Assemble the crostata: Mound the filling in the center of the dough, leaving a 3-inch border all around. Fold the dough over the fruit, pleating as necessary and pressing gently to seal the pleats. Brush the dough with the egg wash.
8 Bake the crostata: Bake for 40 to 45 minutes, or until the apples are tender, the filling bubbles and the crust is golden brown.
Remove from the oven and sprinkle with the reserved cranberries. Place the baking sheet on a wire rack to cool for at least 20 minutes before slicing and serving.