Preheat the oven to 400F degrees and adjust the oven rack to the middle position. Line a baking sheet with a piece of parchment paper.
Transfer the chilled dough to a lightly floured work surface. Roll out into a 9-inch square. Cut the sheet of dough in half both lengthwise and widthwise, to get 4 squares.
Spoon the cherry filling into the middle of each dough square - equally dividing the filling among each square.
Using a pastry brush or your finger, dab a small amount of the beaten egg white onto one of the corners of each dough square. Fold the opposite corner over the filling and press the two corners together, to make a triangle.
Brush the tops of each turnover with the beaten egg white and sprinkle with the coarse sugar (if using).
Transfer the turnovers to the prepared baking sheet. Bake for 20 minutes, or until the turnovers turn golden brown.
Prepare the chocolate drizzle while the turnovers are baking. Place the chocolate chips and milk in a microwave-safe bowl and cook for 30-45 seconds, until the chocolate starts to melt. Remove from the microwave and let it sit for a few minutes for the chocolate to melt further. Then stir until the mix is smooth.
Cool the turnovers on the baking sheet for 5 minutes before transferring to a wire rack to cool further. Drizzle the chocolate over the top of each turnover with a spoon. Or transfer the chocolate ganache to a small plastic baggie and cut one of the corners to create a piping bag.
The turnovers are best served immediately, while still slightly warm. If there are leftovers, store in an airtight container at room temperature for 1 day.