In a bowl, whisk together flour, sugar, and salt. Cut in cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Add ice water 1 tablespoon at a time, mixing just until dough holds together. Shape into a disk, wrap in plastic, and chill for 30 minutes.
In a bowl, combine sliced peaches and blueberries. Add sugar, cornstarch, lemon juice, and vanilla. Toss gently to coat. Set aside.
Preheat oven to 400°F (200°C). Roll out dough on a floured surface into a 10–12 inch circle. Transfer to a parchment-lined baking sheet. Spoon fruit filling into the center, leaving a 2-inch border. Fold edges of dough over the fruit, pleating as needed.
Beat the egg and brush over the crust edges. Sprinkle with extra sugar if desired. Bake for 35–40 minutes until the crust is golden and the filling is bubbling
Let the galette cool slightly before slicing. Serve warm or at room temperature, optionally with whipped cream or vanilla ice cream.