Bring a medium saucepan of water to a boil. Fill a bowl with ice water. Using a sharp paring knife, mark an X on the bottom of each peach or nectarine. Add the peaches to the saucepan and blanch until the skins start to peel away, 1 to 2 minutes. Transfer to the ice bath and let cool. Peel, halve and pit the peaches and cut into 1/2-inch pieces; you should have about 2 cups. Wipe out the saucepan.
In the same saucepan, combine the peaches, sugar, brown sugar, salt cinnamon, lemon zest, lemon juice, and vanilla; bring to a boil. Reduce heat, cook over medium heat, stirring occasionally, until thickened and syrupy, about 8-10 minutes. Scrape the filling into a small bowl; cool to room temperature. Cover and refrigerate until cold, about 1 hour.
Preheat oven to 425 degrees. Line 2 baking sheets with parchment paper.
Remove pie crusts from the packages and allow them to come to room temperature.
Lightly dust your work surface with flour. Unroll pie crusts and cut 6 circles from each crust using a 4-inch biscuit cutter. You’ll have to re-roll the scraps to get the 6th circle.
Place 1 tablespoon of the filling into center of a pie crust circle. Fold in half and press edges together with the tines of a fork to seal. Repeat with remaining circles. Make 3 small slits on top of each hand pies with a knife, to prevent bursting.
Beat egg white with a splash of water in a small bowl until frothy. Brush over the tops of each hand pie. Bake on prepared baking sheets (1-inch apart) for about 15 minutes, until browned.
While pies are baking, whisk together the confectioners’ sugar and milk in a medium bowl until smooth.
Remove cooked pies one at a time from the baking sheet; dip each pie (while warm) into glaze, coating them completely, allowing the glaze to drip back into the bowl.
Place glazed pies on a foil lined baking sheet (for easy clean up) with a wire rack and allow glaze to dry.
Cook’s Note: In a hurry? Pour one (21 oz.) can prepared peach pie filling into a small bowl; dice peaches with a knife and fork. Stir in a 1/2 teaspoon cinnamon. Use in place of homemade filling if desired.