01 - Whisk together flour, sugar, and salt in a large bowl. Cut in cold butter using a pastry cutter or fingers until mixture resembles coarse crumbs. Add ice water 1 tablespoon at a time, stirring just until dough comes together. Divide dough in half, shape into discs, wrap in plastic, and refrigerate for at least 1 hour.
02 - Combine diced strawberries, sugar, cornstarch, lemon juice, and vanilla extract in a medium bowl. Mix gently and set aside.
03 - Preheat oven to 400°F. Line a baking sheet with parchment paper.
04 - Roll chilled dough on lightly floured surface to 1/8 inch thickness. Cut 16 circles using a 4-inch cookie cutter or glass.
05 - Place 8 circles on prepared baking sheet. Spoon about 2 tablespoons strawberry filling onto center of each, leaving border around edges.
06 - Brush edges with beaten egg. Place remaining dough circles over filling. Press edges with fork to seal. Cut small slit on top of each pie to vent steam.
07 - Brush tops with egg wash and sprinkle with sugar if desired.
08 - Bake for 20-25 minutes until golden brown. Cool on wire rack.
09 - Whisk together powdered sugar, milk, and vanilla until smooth. Drizzle over cooled hand pies.