Combine the flour, salt, and sugar in a mixing bowl. Add the cold butter chunks and use your fingers or a pastry cutter to quickly work the butter into the flour until the mixture resembles coarse crumbs with some pea-sized pieces.
Gradually add about 3-4 tablespoons of ice water, mixing gently until the dough just comes together. Press the dough into a rough ball, wrap it in plastic, and chill in the fridge for at least 30 minutes to relax the gluten and keep the butter cold.
Preheat your oven to 400°F (200°C). Remove the chilled dough from the fridge and roll it out on a lightly floured surface into a loose 12-inch circle, about 1/8 inch thick. Don't worry about perfect edges—rustic is perfect here.
Transfer the rolled dough onto a parchment-lined baking sheet. Toss the sliced peaches with lemon juice and a tablespoon of sugar, then arrange them in a slightly overlapping circle in the center of the dough, leaving about 2 inches of border around the edges.
Fold the edges of the dough over the peaches, pleating as you go to create a rustic border. Pinch and press the folds gently to seal, leaving the center exposed to showcase the juicy filling.
Brush the crust with the beaten egg to give it a golden, shiny finish. Place the galette in the oven and bake for about 35 minutes, or until the crust is golden brown and bubbling around the edges.
Remove from the oven and let it cool slightly on the baking sheet. You'll hear a satisfying crackle as the crust cools and juices seep out, creating tiny sizzles and pops.
Slice into thick wedges and serve warm, allowing the flaky crust and juicy peaches to shine. Enjoy the fragrant mess that is a perfect homemade peach galette!
