01 - Whisk together flour, sugar, and salt in a large bowl. Cut in cold butter using a pastry cutter or fingertips until mixture resembles pea-sized crumbs. Gradually add ice water, mixing just until dough holds together. Divide in half, form into 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. Line a baking sheet with parchment paper. On a lightly 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. Lightly brush edges with water, top with remaining rounds, and press edges to seal. Crimp edges firmly with a fork to ensure closure.
05 - Arrange pies on prepared baking sheet. Whisk together beaten egg and milk, brush evenly over pie surfaces. Cut small steam vents in tops of each pie. 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 pies. Allow glaze to set for 15 minutes before serving.