Preheat your oven to 400°F, positioning a rack in the center. Dampen your work surface and place a 15×15-inch sheet of parchment paper on it. Lightly sprinkle the parchment with flour.

Roll out the pie dough on the floured parchment until it reaches a 14-inch diameter. Use a fork to prick a few holes in the center of the dough.

Transfer the dough, still on the parchment, onto a baking sheet and place it in the freezer to chill while you prepare the peaches.

Slice the peaches, leaving the skin on, into 1/2 inch thick segments. Place the slices in a large bowl, drizzle with vanilla extract, and mix to coat.

Combine the sugar and cornstarch, then sprinkle this mixture over the peaches. Gently toss to evenly coat the peach slices.

Place the peaches in a mesh sieve set over the large bowl to macerate, allowing them to release their juices for about fifteen minutes.

Transfer the collected juices to a small pot over medium heat and bring to a simmer without stirring. Swirl the pot occasionally until the juices thicken, then remove from heat.

Retrieve the chilled pie dough from the freezer and arrange the peach slices on it, starting from the center and working outward, leaving a four-inch border. Pour the thickened juice over the peaches.

Fold the edges of the dough over the peaches, creating pleats as needed. Lightly brush the top of the galette with a thin layer of heavy cream.

Bake for 40 minutes or until the crust turns golden and crispy.

Allow the galette to cool on the baking sheet for fifteen minutes before serving. Use the edges of the parchment paper to lift it off the sheet pan for easy serving.