In a food processor, combine the flour, 1 tablespoon sugar and ½ teaspoon salt. Pulse 3 or 4 times. Scatter 42 grams (3 tablespoons) butter over the flour mixture and process until well incorporated, 15 to 20 seconds. Scatter in the remaining butter and pulse until the mixture resembles coarse sand with tiny, pebbly bits. Transfer to a large bowl.

Add 2 tablespoons ice water, then fold and toss with a silicone spatula until incorporated. Add another 1 tablespoon ice water and fold again. Continue adding water and folding until a cohesive, evenly moistened dough forms and no floury bits remain. If in doubt, err on the side of too much water than too little.

Using your hands, form the dough into a ball and dust with flour. Set it on the counter and press it into a disk 5 inches in diameter, then wrap tightly in plastic. Refrigerate for at least 1 hour or up to 2 days.

When ready to bake, heat the oven to 450°F with a rack in the lowest position. Line a rimmed baking sheet with kitchen parchment. If the dough is too firm to roll out, let stand at room temperature 5 to 10 minutes until malleable.

Lightly flour the counter, unwrap the dough and dust it with flour. Using a rolling pin, roll it into an 11-inch circle, lightly dusting with flour as needed. Sprinkle 1 tablespoon of the remaining sugar on the dough and, using your hands, spread in an even layer to the edges. Roll the dough, pressing the sugar into it, until the circle is 12 inches in diameter.

Flip the dough, sugared side down, onto the center of the prepared baking sheet; it’s fine if the edges slightly climb up the sides of the baking sheet. If the dough is very soft, lay plastic wrap against the surface and refrigerate for a few minutes to firm, or for up to 24 hours. (If refrigerated until very cold and stiff, let stand at room temperature until pliable but still cool.)

In a large bowl, combine the remaining 3 tablespoons sugar, remaining pinch of salt and lemon zest. Using your fingers, rub the zest into the sugar until evenly moistened. Add the peaches and berries, then toss.

Mound the fruit mixture in the center of the dough, keeping 1½ to 2 inches around the edge uncovered. Working in one direction around the circumference of the dough, fold the edge toward the center up and over the filling, pleating it at intervals. Gently press the pleats so they remain in place. Refrigerate, uncovered, for 10 to 15 minutes (no longer or the fruit may begin to release too much juice).

Bake until the crust is deep golden brown, 25 to 30 minutes, rotating the baking sheet halfway through. Cool on the baking sheet on a wire rack for 15 minutes. Slide a wide metal spatula under the crostata to loosen it from the parchment, then transfer it to a platter. Serve warm or at room temperature.