Step 1: In a large bowl, whisk together the flour, sugar, and salt. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs with some pea-sized pieces.
Step 2: Gradually add ice water, one tablespoon at a time, mixing until the dough just begins to come together. Form into a disk, wrap in plastic, and refrigerate for at least 1 hour.
Step 3: Preheat your oven to 400°F (200°C). In a medium bowl, toss the sliced peaches and mixed berries with 1/3 cup sugar, cornstarch, and lemon juice.
Step 4: Roll out the chilled dough on a piece of parchment paper to a 12-inch circle. Transfer the parchment and dough to a baking sheet.
Step 5: Mound the fruit mixture in the center of the dough, leaving a 2-inch border. Fold the edges of the dough over the fruit, pleating as you go.
Step 6: Brush the edges of the crust with the beaten egg and sprinkle with turbinado sugar. Bake for 35-40 minutes until the crust is golden and the fruit is bubbling.
Step 7: Allow the galette to cool on the baking sheet for at least 20 minutes before serving.