In a large bowl, whisk together flour, salt, and sugar. Cut in cold butter until mixture resembles coarse crumbs. Drizzle in ice water, one tablespoon at a time, mixing until dough holds together. Shape into two discs, wrap, and refrigerate for 30 minutes.
Peel and dice peaches into 1/4 inch pieces. In a medium bowl, combine peaches with granulated sugar, brown sugar, lemon juice, cinnamon, nutmeg, cornstarch, and salt. Let sit for 10-15 minutes, then stir again before using.
Roll one dough disc to 1/8 inch thickness on a floured surface. Cut out 4-5 inch circles with a round cutter. Repeat with second disc, rerolling scraps once. You should have about 20 circles total.
Place 2 tablespoons of filling in the center of half the circles. Brush edges with egg wash. Top with remaining circles, press to seal, and crimp edges with a fork. Cut 2-3 small slits in the top of each pie.
Place assembled pies on a parchment-lined baking sheet and refrigerate for 15 minutes. Meanwhile, preheat oven to 400°F (200°C).
Brush chilled pies with remaining egg wash and sprinkle with turbinado sugar. Bake for 18-20 minutes until golden brown and filling is bubbly. Cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Whisk powdered sugar, milk, and almond extract until smooth. Drizzle glaze over cooled hand pies. Let set for 10 minutes before serving.