To make the pie dough: In the bowl of a stand mixer fitted with the paddle attachment, mix the flour, sugar, and salt on low speed just to combine.
Add the butter, mixing first on low and then increasing the speed to medium low.
With the mixer on low, gradually add the cold water, beating just until the dough comes together.
Turn the dough out onto your work surface. Divide it in half and shape each piece into a disk. Wrap each in plastic wrap and refrigerate for at least 30 minutes before using.
Preheat your oven to 400 degrees Fahrenheit. Line two baking sheets with parchment paper or a Silpat baking mat.
In a medium bowl, combine the strawberries, sugar, and cornstarch. Stir until well coated.
Remove one disk of dough from the refrigerator. Place it on a lightly floured work surface and roll it out into a square about 1/8-inch thick.
Cut the dough into 4 equal pieces, about 5x5 squares. Spoon about 2 tablespoons of the strawberry mixture into the center of each square, then top with about 1 tablespoon of chopped dark chocolate.
Brush the edges of the square with heavy cream. Bring opposite corners together to form a triangle and press the edges together. Use a fork to crimp the edges of the pie.
In a small bowl, combine the egg and water with a fork. Brush the top with the egg wash and sprinkle with turbinado sugar.
Transfer the hand pies to the prepared baking sheets. Cut a small vent or two in the tops of each pie.
Bake for 20 minutes, or until golden brown. Transfer to a wire rack and allow them to cool completely.