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 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 let 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 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 dough rounds. Press edges firmly to seal, then crimp with a fork to ensure closure.
05 - Transfer pies to prepared baking sheet. Whisk together beaten egg and milk, then brush over each pie. Cut a small vent slit in the top of each pie. Bake for 22-25 minutes until golden brown. Cool on wire rack for at least 15 minutes.
06 - Whisk powdered sugar, 2 tablespoons milk, and vanilla extract in a small bowl until smooth. Add additional milk 1 teaspoon at a time if needed to achieve drizzling consistency. Drizzle over cooled pies and allow glaze to set for 10 minutes before serving.