Preheat your oven to 400°F (200°C).

Roll out the refrigerated pie crust onto a sheet of parchment paper, shaping it into a 12-inch circle. Transfer to a rimmed half-sheet pan.

In a large mixing bowl, combine fresh lemon juice and vanilla extract, whisking in the cornstarch until smooth. Add granulated sugar, brown sugar, and cinnamon, stirring gently.

Add sliced peaches to the bowl with the lemon-sugar mixture and gently toss to coat.

Arrange the coated peaches in the center of the pie crust, leaving a 2-inch border. Pour remaining juices over the peaches.

Fold the edges of the crust over the fruit, crimping lightly. Dot exposed fruit with small pieces of butter.

Brush the exposed crust with an egg wash made from a beaten egg mixed with milk. Sprinkle coarse sugar on top.

Bake for 25-30 minutes until the crust is golden brown and peach juices are bubbling.

Let the galette cool for about 5 minutes before serving.