In a large mixing bowl, whisk together the flour, sugar, and salt. Add the cold, cubed butter and use a pastry cutter or your fingers to work the butter into the flour until the mixture resembles coarse crumbs with some pea-sized pieces. Chill the dough in the fridge for at least 30 minutes to relax.
Meanwhile, prepare the peaches by washing, pitting, and slicing them into thick slices. Toss the sliced peaches with lemon juice and sugar, then set aside to macerate and release their juices.
Preheat your oven to 400°F (200°C). Once the dough is chilled, transfer it onto a lightly floured surface and gently roll it into a rough 12-inch circle, about 1/8-inch thick. Transfer the rolled dough onto a parchment-lined baking sheet.
Arrange the thick peach slices in the center of the dough, leaving about a 2-inch border. Spoon some of the accumulated juice over the peaches, and sprinkle with sliced almonds if using. Fold the edges of the dough over the fruit in a rustic, uneven manner, pinching any cracks closed.
In a small bowl, beat the egg with water to create an egg wash. Brush this over the exposed crust for a glossy, golden finish.
Bake the galette in the preheated oven for about 45 minutes, until the crust is golden brown and the peaches are bubbling and caramelized at the edges. Check halfway through and cover the edges with foil if they brown too quickly.
Remove the galette from the oven and let it cool slightly for 10 minutes. The crust will be flaky and crisp, while the peaches remain juicy and caramelized. Serve warm, sliced into wedges, and enjoy the rustic, sweet-tart flavors.
