Mix the flour and a pinch of salt in a large bowl. Add the cold butter, either grated or cut into small pieces, and quickly work it into the flour using your fingertips or a pastry cutter until the mixture resembles coarse crumbs with some pea-sized pieces.
Gradually add cold water, one tablespoon at a time, mixing gently until the dough just comes together. Be careful not to overmix; the dough should be crumbly but hold together when pressed.
Form the dough into a flat disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes to keep the butter cold and relax the gluten.
While the dough chills, prepare the peaches by washing and slicing them thick. Toss the slices with sugar, lemon juice or zest, and optional spices until evenly coated.
Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper. Remove the dough from the fridge and let it sit for a few minutes to soften slightly.
Roll out the chilled dough on a lightly floured surface into a roughly 12-inch circle, about 1/8 inch thick. Keep the dough cold and handle it quickly to prevent melting the butter.
Transfer the rolled dough onto the prepared baking sheet. Arrange the peach slices in the center, leaving about 2 inches around the edges for folding.
Fold the edges of the dough over the peaches, pleating as needed to create a rustic border. Brush the exposed crust with beaten egg for a shiny, golden finish.
Bake the galette in the preheated oven for about 40 minutes, or until the crust is golden brown and crisp, and the peaches are bubbling at the edges.
Remove from oven and let cool slightly before slicing. The crust should be flaky and crisp, with caramelized, juicy peach filling inside. Serve warm or at room temperature and enjoy the burst of fruity flavors with every bite.
