Make the crust: In a large bowl, mix together ¾ cup (95 g) all-purpose flour, the whole wheat flour, and salt. Add the butter and, using a pastry cutter, work it into the flour until only pea-sized pieces remain. Continue working with your hands until the dough is shaggy.
Add the water, starting with 3 tablespoons, and mix until the dough is moist enough to hold together. Add more water as needed, 1 tablespoon at a time. Form the dough into a disc and wrap with plastic wrap. Refrigerate for 30–60 minutes.
Preheat the oven to 375˚F (190˚C). Line a baking sheet with parchment paper.
While the dough is resting, make the filling: In a medium bowl, combine the blackberries, cherries, peaches, sugar, and remaining 2 tablespoons of flour. Toss to coat the fruit.
Assemble the crostata: On a lightly floured surface, roll the dough out to a 12-inch (30 cm) wide circle, about ⅛ inch (3 mm) thick. Transfer the dough to the prepared baking sheet.
Spoon the fruit filling into the center of the dough, leaving a 2-inch (5 cm) border around the edges. Fold the edges of the crust up and over the filling to create a rustic look. Brush the crust with the beaten egg and sprinkle with sugar.
Bake for 45–50 minutes until the crust is golden brown.
Let cool for 10–15 minutes before slicing and serving.