Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper. Lightly flour your work surface and roll out the chilled pie crust into a rough 12-inch circle. Transfer the crust to the prepared baking sheet.
In a mixing bowl, gently toss the thinly sliced peaches with lemon juice and 2 tablespoons of sugar. Let sit for about 10 minutes to allow the juices to release and the flavors to meld.
Spread a handful of sliced almonds or frangipane (if using) in the center of the dough, leaving a 2-inch border around the edges. Arrange the peach slices neatly over the almonds, overlapping slightly for a layered look.
Fold the edges of the dough over the peaches, pleating as you go, to create a rustic, freeform crust. Dot the exposed fruit with small cubes of cold butter for extra flakiness.
Brush the crust with the beaten egg to give it a shiny, golden finish. Sprinkle a light dusting of sugar over the crust and fruit for caramelization.
Bake in the preheated oven until the crust is golden brown and crispy, and the peaches are bubbling and caramelized, about 40 minutes. Cover the edges with foil if they brown too quickly.
Remove the galette from the oven and let it cool slightly on a wire rack. The crust will crackle as it cools, revealing a juicy, fragrant filling inside.
Slice into wedges and serve warm, enjoying the crispy crust and luscious, bubbling peach filling in every bite.
