In a food processor, pulse together the flour, sugar, and salt until combined. Add the chilled cubed butter and shortening, pulsing until the mixture resembles coarse breadcrumbs with pea-sized pieces of fat visible throughout—this creates the flaky texture we want. Add the ice-cold water one tablespoon at a time, pulsing gently after each addition until the dough just comes together without being wet or sticky. Divide the dough into two equal discs, wrap each in plastic wrap, and refrigerate for at least 30 minutes while you prepare the filling.

Peel and dice the peaches into 1/2-inch pieces and place them in a bowl with 1/2 cup sugar. Let them sit for 1 hour to release their juices—this maceration step concentrates the peach flavor and creates a syrup base. After an hour, strain the peach juice into a small saucepan, reserving the fruit. Whisk together the cornstarch, cinnamon, and salt, then add this mixture to the peach juice, stirring until smooth. Bring the mixture to a boil over medium heat and cook for 2 minutes, stirring constantly, until it thickens into a glossy syrup. Remove from heat and stir in the lemon juice, vanilla extract, and almond extract, then fold in the reserved diced peaches. Allow the filling to cool to room temperature—I like to spread it on a plate to speed up cooling, which prevents the dough from getting warm when we assemble the pies.

Remove one disc of dough from the refrigerator and let it sit at room temperature for 10-15 minutes until it's pliable enough to roll without cracking. On a lightly floured surface, roll the dough to 1/8-inch thickness—thin enough to be delicate but sturdy enough to hold the filling. Using a 4-inch round cutter (or drinking glass), cut out as many circles as possible, then gather scraps, re-roll, and cut again. Repeat with the second dough disc. You should have approximately 12-16 circles depending on how efficiently you cut.

Whisk together the egg and milk to create an egg wash. Working with one dough circle at a time, brush the edges lightly with the egg wash, then place 1 tablespoon of cooled peach filling slightly off-center on the circle. Fold the dough in half over the filling, gently pressing the edges together to seal, then crimp the sealed edge firmly with the tines of a fork to create a decorative pattern and ensure a tight seal. Transfer the sealed pie to a parchment-lined baking sheet and repeat with the remaining dough circles and filling. Once all pies are assembled, use a sharp knife to cut two small slits in the top of each pie to allow steam to escape during baking. Refrigerate the assembled pies for 30 minutes—this chilling prevents them from puffing up unevenly and helps them maintain their shape.

Preheat your oven to 350°F. Brush the exterior of each chilled pie with the remaining egg wash to create an even golden-brown finish. Arrange the pies on the parchment-lined baking sheet, leaving about 1 inch between each one, and bake for 30 minutes until the pastry is deep golden brown and the filling is bubbling slightly through the steam vents. Remove from the oven and transfer the pies to a wire rack to cool completely—I find that letting them cool completely allows the filling to set properly, so each bite holds together nicely.

While the pies cool, prepare the glaze by whisking together the sifted powdered sugar, milk or heavy cream, and almond extract until smooth and pourable. Once the hand pies have cooled completely, drizzle the glaze generously over the top of each pie, allowing it to pool slightly in the crevices. Serve at room temperature or slightly warm.