In a large bowl, whisk together the flour, sugar, and salt. Cut in the cold butter until the mixture resembles coarse crumbs with some pea-sized pieces remaining.

Gradually add the ice water, mixing until the dough just comes together. Form the dough into a disk, wrap it in plastic, and refrigerate for at least 30 minutes.

In a separate large bowl, gently toss the sliced peaches with sugar, cornstarch, lemon juice, and vanilla extract until evenly coated.

Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

On a lightly floured surface, roll out the chilled dough into a 12-inch circle. Carefully transfer the dough to the prepared baking sheet.

Arrange the peach filling in the center of the dough, leaving a 1.5-inch border. Fold the edges of the dough over the peaches, pleating it as you go.

Brush the crust with the beaten egg and sprinkle with turbinado sugar. Bake for 40-50 minutes, or until the crust is golden brown and the filling is bubbly.

Let the galette cool on the baking sheet for at least 15 minutes before transferring it to a wire rack to cool completely. Serve warm or at room temperature, optionally with a scoop of vanilla ice cream.