Preheat the oven to 425°F. Line a baking sheet with parchment paper.
Lightly flour your work surface then unfold the puff pastry. Using a rolling pin, roll it until it’s a 10-inch square. Round off the corners (if desired) then transfer the pastry onto the prepared baking sheet.
In a small bowl, stir together granulated sugar, flour and cinnamon. Slice peaches into ½″ thick slices, place peaches in a medium bowl and sprinkle with flour mixture. Add vanilla and stir gently with a spatula until the flour is fully incorporated.
Arrange the peaches in a circular pattern over the dough working from the outside in and leaving a 2″ dough border. Discard any excess juices from the peaches, or your galette may overflow. Dot the top of the peaches with small chunks of ½ tbsp butter. Fold the border up over the peaches, pinching together the overlapping edges. Try to patch up any cracks in the dough.
Brush the crust with beaten egg and sprinkle with sugar. Bake for 25-30 minutes until the crust is golden brown and the peach juices are syrupy. Let sit 15 minutes before serving.
