01 - Whisk together flour, sugar, and salt in a large bowl. Cut in cold butter using a pastry cutter or fingertips until mixture resembles coarse crumbs. Gradually add ice water, mixing just until dough holds together. Divide dough 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.
03 - Preheat oven to 375°F. Line a baking sheet with parchment paper. On a floured work surface, roll each dough disk to approximately 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 and top with remaining rounds. Press edges firmly to seal and crimp with a fork for a decorative finish.
05 - Transfer pies to prepared baking sheet. Whisk together egg and milk, then brush over each pie. Cut small steam vents in the tops. Bake for 22-25 minutes until golden brown. Cool on wire rack.
06 - Whisk powdered sugar, milk, and vanilla extract in a small bowl until smooth and drizzling consistency. Drizzle glaze over cooled pies and allow to set before serving.