In a food processor, combine all-purpose flour, granulated sugar, and salt. Add cold, unsalted butter cut into small cubes and pulse until the mixture resembles coarse crumbs, about 10-15 seconds. Gradually add cold water, pulsing until the dough begins to form a cohesive disc. Wrap it in plastic wrap and refrigerate for at least 1 hour.

While your dough chills, preheat the oven to 425°F (190°C). Prepare a baking sheet by lining it with parchment paper.

In a mixing bowl, gently combine sliced ripe peaches, light brown sugar, cornstarch, and vanilla extract. Toss until well-coated and let sit for about 10 minutes.

Once the dough has chilled, roll it out on a lightly floured surface to approximately ⅛ inch thick. Transfer to the prepared baking sheet.

Spoon the peach filling into the center of the dough, leaving about a 3-inch border. Fold the edges over the filling and seal. Brush with a beaten egg and top with almond slices.

Place the galette in the preheated oven and bake for 25-28 minutes until the crust is golden brown and juices are bubbling.

Allow the galette to cool for at least 15 minutes on the baking sheet before serving.