Preheat your oven to 400°F (200°C) and have a sturdy rimmed half-sheet pan ready.

Unroll the refrigerated pie crust on parchment paper and roll it into a 12-inch circle. Transfer it to the prepared half-sheet pan.

In a medium mixing bowl, whisk together lemon juice, vanilla extract, cornstarch, granulated sugar, brown sugar, and ground cinnamon until smooth.

Add the sliced peaches to the bowl and gently toss to coat them evenly with the syrup.

Arrange the peach filling in the center of the dough, leaving a 2-inch border around the edges. Pour any remaining syrup over the peaches.

Fold the edges of the crust over the peaches, crimping as necessary to secure the filling.

Dot the filling with butter, whisk together the egg and milk, and brush this mixture over the crust. Sprinkle coarse sugar on top.

Bake for 25-30 minutes or until the crust is golden-brown. Continue baking for an additional 5 minutes if necessary.

Remove from the oven and allow to cool for 5 minutes on the pan before serving.