01 - Whisk flour, sugar, and salt in a large bowl. Cut cold butter into the mixture using a pastry cutter or fingertips until pea-sized crumbs form. Gradually add ice water, mixing just until dough holds together. Divide into two disks, wrap in plastic, and refrigerate for 30 minutes.
02 - Combine strawberries, sugar, lemon juice, and cornstarch in a medium saucepan. Cook over medium heat, stirring constantly, for 5-7 minutes until mixture thickens. Remove from heat and allow to cool completely before using.
03 - Preheat oven to 375°F and line a baking sheet with parchment paper. On a floured surface, roll each dough disk to 1/8-inch thickness. Cut into 4-5 inch rounds, yielding 8-10 rounds total.
04 - Place 2 tablespoons of cooled strawberry filling in the center of half the dough rounds. Brush edges with water and top with remaining rounds. Press edges firmly to seal and crimp with a fork for decorative finish.
05 - Arrange pies on prepared baking sheet. Whisk beaten egg with milk and brush over pastry tops. Cut small slits in each pie for steam release. Bake for 22-25 minutes until golden brown. Transfer to wire rack to cool completely.
06 - Whisk powdered sugar, milk, and vanilla extract in a small bowl until smooth and pourable. Drizzle glaze over cooled hand pies and allow to set for 10-15 minutes before serving.