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, and mix, first on low and then increasing the speed to medium low, cutting the butter into the flour until the mixture resembles small peas. With the mixer on low, 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 oven to 400 degrees F. Line two baking sheets with parchment paper or a Silpat baking mat. In medium bowl, combine the strawberries, sugar, and cornstarch. Stir until strawberries are well coated.
Remove the pie dough from the refrigerator. Place one of the disks on a lightly floured work surface. Roll into a square about 1/8-inch thick. Cut the dough into 4 equal pieces, about 5x5 squares. Spoon about 2 tablespoons of strawberries into the center of each square, then top with about 1 tablespoon of chopped dark chocolate. Brush the edges of the square with the 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 of the pie with the egg wash and sprinkle generously with turbinado sugar. Repeat with the remaining squares of dough. Roll out the second disk of pie dough and do the same.
Transfer the hand pies to the prepared baking sheets, you should have 8 hand pies. Using a sharp knife, cut a small vent or two in the top of each pie. Bake for 20 minutes, or until the pies are golden brown. The filling may bubble out a bit and that's ok. Transfer to a wire rack and allow the pies to cool completely.