Start by preparing the crust: in a mixing bowl, combine the flour and cold butter. Use your fingers or a pastry cutter to work the butter into the flour until the mixture resembles coarse crumbs with pea-sized pieces. Add ice water gradually, mixing until the dough just comes together.
Shape the dough into a flat disk, wrap it tightly in plastic wrap, and chill in the refrigerator for at least 1 hour to relax the gluten and keep the butter cold for flaky layers.
While the dough chills, peel and slice the peaches into thin, even slices. Toss them in a bowl with granulated sugar and lemon juice, then set aside to macerate for about 15 minutes, allowing the peaches to release their juices and become fragrant.
Preheat your oven to 400°F (200°C). Lightly flour a clean surface and roll out the chilled dough into a 12-inch circle, about 1/8 inch thick. Transfer it to a parchment-lined baking sheet.
Arrange the peach slices in the center of the dough, leaving about a 2-inch border. Fold the edges of the dough over the fruit, pleating as needed to create a rustic, free-form crust. Be gentle to prevent tearing.
Brush the exposed crust with the beaten egg to give it a glossy, golden finish. If desired, sprinkle toasted almonds or nuts over the peaches for added crunch.
Place the galette in the oven and bake for about 40 minutes, or until the crust is deep golden brown and bubbling around the edges. Keep an eye on it to prevent over-browning, tenting with foil if necessary.
Remove the galette from the oven and let it cool slightly for about 10 minutes. The filling will thicken slightly as it cools, and the crust will set to a crisp, flaky texture.
Slice and serve the peach galette warm or at room temperature, enjoying the crispy crust and the juicy, fragrant peaches with each forkful.
