01 - In a large bowl, whisk together the flour, sugar, and salt. Cut in the cold cubed butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Gradually add ice water, 1 tablespoon at a time, mixing gently just until the dough comes together. Divide the dough in half, shape each portion into a flat disc, wrap tightly in plastic, and refrigerate for at least 30 minutes.
02 - While the dough chills, combine the diced peaches, granulated sugar, lemon juice, and cinnamon in a small saucepan. Bring to a simmer over medium heat, stirring frequently. Dissolve the cornstarch in 2 teaspoons of water and stir it into the peach mixture. Continue cooking for 2 to 3 minutes until the filling thickens. Remove from heat and let cool completely.
03 - Preheat the oven to 375°F. Line a baking sheet with parchment paper and set aside.
04 - On a lightly floured surface, roll out each chilled dough disc to 1/8-inch thickness. Cut each disc into 8 rectangles, approximately 3 by 4 inches, yielding 16 total rectangles.
05 - Place 8 dough rectangles on the prepared baking sheet. Spoon 1 to 2 tablespoons of cooled peach filling onto each rectangle, leaving a 1/4-inch border around the edges. Brush the borders lightly with beaten egg. Lay the remaining 8 rectangles on top and press the edges firmly to seal. Crimp the edges with a fork to ensure they stay closed.
06 - Brush the tops of each assembled pastry with the remaining egg wash. Use a fork to poke 2 to 3 small holes in the top of each pastry to allow steam to escape during baking.
07 - Bake in the preheated oven for 18 to 22 minutes, or until the pastry is golden brown. Transfer to a wire rack and allow to cool completely before glazing.
08 - In a small bowl, whisk together the powdered sugar, milk, vanilla extract, and peach jam if using, until smooth and drizzly. Spoon or drizzle the glaze over the cooled pastries. Let the glaze set for 15 to 20 minutes before serving.