Preheat your oven to 400°F (200°C) and prepare a baking sheet lined with parchment paper.
In a mixing bowl, combine sliced peaches, lemon juice, sugar, vanilla extract, and corn starch. Toss gently to coat the peaches and set aside to macerate for about 15 minutes.
On a lightly floured surface, roll out the pie crust to about a 12-inch diameter. Transfer it onto the prepared baking sheet.
Spoon the peach mixture into the center of the dough, leaving a 2-inch border around the edges.
Carefully fold the edges of the crust over the peaches, pleating as you go to create a rustic look.
Beat the egg and brush the mixture over the exposed crust for a golden finish. Sprinkle coarse sugar on top of the crust for added crunch.
Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown and the peaches are bubbly.
Remove from oven and let cool for about 10 minutes before slicing. Garnish with fresh mint leaves if desired.
Notes
Adjust sugar based on the sweetness of the peaches.