In a large bowl, combine flour, 1 tbsp sugar, and salt. Add cold butter and mix with your fingers until the mixture resembles coarse crumbs.
Add 2-4 tablespoons of cold water, just enough to bring the dough together. Form the dough into a disc, wrap in plastic, and refrigerate for at least 30 minutes.
Preheat oven to 400°F (200°C). Roll out the dough on a floured surface to a 12-inch circle. Transfer to a baking sheet.
In a bowl, toss sliced peaches with remaining sugar, lemon juice, and cornstarch until well coated. Arrange the peaches in the center of the dough, leaving a 2-inch border.
Fold the edges of the dough over the peaches, pleating as necessary. Brush the crust with milk.
Bake in the preheated oven for 40-45 minutes, or until the crust is golden brown and the peaches are tender and bubbly.
Allow the galette to cool slightly before slicing and serving.