In a large bowl, whisk together 2 cups of all-purpose flour and ½ teaspoon of salt. Cut in 1 cup of cold, unsalted butter until the mixture resembles coarse crumbs. Gradually add 6-8 tablespoons of ice water, stirring until a dough forms. Shape it into a disk, wrap in plastic wrap, and refrigerate for at least 30 minutes.

While the dough chills, slice 4-5 fresh peaches and place them in a mixing bowl. Add ½ cup of granulated sugar, 2 tablespoons of cornstarch, 1 tablespoon of lemon juice, ½ teaspoon of cinnamon, and 1 teaspoon of vanilla extract. Gently toss the mixture until the peaches are well coated.

Preheat your oven to 400°F (200°C). Roll out the chilled dough into a 12-inch circle. Transfer the rolled dough to a parchment-lined baking sheet. Spoon the peach mixture into the center, leaving a 2-inch border. Fold the edges of the dough over the filling to form a rustic tart.

Beat 1 egg and brush it over the exposed dough edges for a golden finish. Sprinkle coarse sugar over the crust for added texture.

Place the tart in the preheated oven and bake for 35-40 minutes until the crust is golden brown and the peaches are bubbly.

Remove the tart from the oven and allow it to cool for at least 15 minutes before serving, either warm or at room temperature.