In a medium bowl, mix together all of the ingredients with a rubber spatula. Let sit outside, covered for about 30 minutes.
Empty the bowl of ingredients into a medium saucepan set on medium heat. Mix to combine and bring to a boil, stirring occasionally. Boil for about 5 to 7 minutes, until the mixture looks thick.
Let the mixture cool completely before putting in an airtight container. Place in the fridge for at least 4 to 6 hours.
In a large bowl, whisk together the flour, cardamom, salt and sugar. Add the cold butter and, with a pastry blender or your fingers, cut the butter until the chunks are pea-sized and coated in flour.
In a medium bowl, mix the water, ice and apple cider vinegar. Add 2 tablespoons of this cold water mixture to the flour mixture using the pastry blender or your hands to mix. Continue adding 2 tablespoons of the cold liquid at a time until the dough just starts to come together.
Divide the dough into two equal parts. Wrap each portion in plastic wrap. Pat and shape the dough to form neat rectangles, about 5 by 6 inches in size each.
Refrigerate dough for 1 hour.
Take one rectangle of dough out of the fridge. Dust a work surface with flour. Unwrap the dough and roll it out roughly into an 11-by-14-inch rectangle with a thickness of ⅛ to ¼ inch.
Using a ruler and a sharp knife, trim the rough edges to form a smooth rectangle. Set the trimmings aside.
Cut the dough lengthwise in 3-inch sections. Then cut it across widthwise in 3½-inch sections to get 8 pieces.
Place the pieces of dough on a parchment-lined baking sheet and place in the freezer for 10 minutes.
Repeat the cutting and chilling process for the second rectangle of dough.
Collect all of the scrap pieces of dough and wrap in a plastic wrap. Form a rectangle and refrigerate for 30 minutes.
In a small bowl, whisk together the egg, water and sugar until well combined.
Remove the first baking sheet. Using a pastry brush, brush the edges of each rectangle (about ½ inch all around) with the egg wash.
Spoon about 1 to 1¼ heaping tablespoons of the filling in the center of each pie, leaving a ½ to ¾-inch gap around the filling.
Remove the second baking sheet from the freezer, and place each piece gently on top of a rectangle with filling. Use your fingertips to gently press around the filling to seal the pie.
Brush the top of each pie with egg wash.
Use a spatula to place the pies on a baking sheet, and freeze until ready to bake.
Take the scrap dough from the fridge. Roll it out into a rectangle with a thickness of ⅛ to ¼ inch, and cut into 4 rectangles. Repeat the steps of filling and forming pies, applying egg wash on top, to form 2 additional hand pies.
Meanwhile, preheat the oven to 375 degrees.
Remove the pies from the freezer and apply one more layer of egg wash to the tops. Cut an X with a sharp knife in the middle of the top layer of dough of each pie so that steam can escape while it bakes.
Bake for 30 minutes, or until golden brown in color.
Remove from the oven, transfer to a wire rack and let cool completely.
In a medium bowl, whisk together the powdered sugar, strawberry powder, vanilla extract and milk until it is a thick yet spreadable consistency.
Spread about 2 teaspoons of icing on each pie, and decorate with some sprinkles. Let the pies sit for 30 minutes so the icing sets. Serve.
