In a large mixing bowl, whisk together the flour, sugar, and salt. Add the cold butter and cut it into the flour mixture until crumbly with small butter pieces throughout.
Gradually mix in the ice water, one tablespoon at a time, until the dough starts to come together.
Divide the dough into two equal portions, shape into discs, wrap tightly, and refrigerate for at least 30 minutes.
Make the Cream Cheese Filling:
In a small bowl, combine the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy.
Roll and Cut:
Preheat the oven to 375°F. Line a large baking sheet with parchment paper.
Roll out one dough disc on a lightly floured surface until about ⅛-inch thick. Slice into equal-sized rectangles. Repeat with the remaining dough.
Fill the Pastries:
Arrange half of the rectangles on the prepared baking sheet. Add a spoonful of the cream cheese mixture to the center of each, then top with a spoonful of strawberry pie filling. Be careful not to overfill.
Place the remaining dough rectangles on top and gently seal the edges using a fork.
Add Egg Wash:
Whisk together the egg and milk. Brush the tops of the pastries and poke a few holes in the tops with a fork to allow steam to escape.
Bake:
Bake for 22–25 minutes or until the pastries are golden brown and flaky. Let cool for 10–15 minutes before glazing.
Glaze and Serve:
Whisk together the powdered sugar, milk, and vanilla extract until smooth. Drizzle over the cooled pastries and allow the glaze to set before serving.