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 one 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 dough circles on prepared baking sheet. Spoon about 2 tablespoons strawberry filling onto center of each, leaving border around edges. Brush edges with beaten egg. Place remaining dough circles over filling to form pies. Press edges with fork to seal. Cut small slit on top of each pie to vent steam.
06 - Brush tops with egg wash and sprinkle with sugar if desired.
07 - Bake for 20-25 minutes until golden brown. Cool on wire rack.
08 - Whisk together powdered sugar, milk, and vanilla in small bowl until smooth. Drizzle over cooled hand pies.