Prepare the Crust: In a large bowl, whisk together flour, 1 tsp sugar, and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.

Gradually sprinkle in the ice water, mixing until the dough just begins to come together. Do not overmix. Form the dough into a disk, wrap tightly in plastic wrap, and chill for at least 30 minutes.

Prepare the Filling: In a separate bowl, gently toss the blueberries, sliced peaches, 1/2 cup sugar, cornstarch, lemon juice, and vanilla extract until the fruit is evenly coated. Set aside.

Assemble the Galette: Preheat oven to 400°F (200°C). On a lightly floured surface, roll the chilled dough into a roughly 14-inch circle. Carefully transfer the dough to a parchment-lined baking sheet.

Arrange the fruit filling in the center of the dough, leaving a 2-inch border around the edge. Fold the edges of the dough up and over the fruit mixture, creating overlapping pleats.

Brush the folded crust edges generously with the egg wash and sprinkle the crust and fruit lightly with coarse sugar.

Bake for 35 to 40 minutes, or until the crust is golden brown and the fruit juices are visibly bubbling thickly. Let cool on the baking sheet for at least 15 minutes before slicing and serving warm.