Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a medium mixing bowl, combine the sliced peaches with lemon juice, granulated sugar, vanilla extract, and corn starch. Toss gently and let macerate for 15 minutes.
Lightly flour your work surface and roll out the pie crust to a circular shape approximately 12 inches in diameter. Transfer it to the prepared baking sheet.
Spoon the peach mixture into the center of the dough circle, leaving a 2-inch border around the edges.
Fold the edges of the crust over the peach filling, creating pleats for a rustic appearance.
Beat the egg to create an egg wash and brush it over the exposed crust. Sprinkle coarse sugar on top.
Bake in the preheated oven for 25-30 minutes until the crust is golden brown and the peaches are bubbling.
Allow the galette to cool on the baking sheet for about 10 minutes before serving. Garnish with fresh mint leaves if desired.
Notes
Serve warm or at room temperature, with a scoop of vanilla ice cream for an indulgent treat.