Once your dough is chilled, cut it in half. Then roll one half out in a long rectangle that is about 24″ long and 8″ wide. One batch of this rough puff will make about 12 apple turnovers.
Place the dough onto a baking sheet lined with parchment paper.
Use a 4-inch ring to cut three or four equal circles out of the dough. You can also use a sharp knife or a pizza cutter if you don't have a circle. This dough cannot be rolled out again, but if you slice up the rest of the dough into strips, twist them, and bake them with some butter and a cinnamon sugar mix for delicious cinnamon sticks.
Repeat with the other half of the dough.
Dock the dough circles with a fork so that they don't overdevelop in the oven.
Mix an egg and water together in a small bowl and use a pastry brush to brush the egg wash halfway around the outside of the circle.
Scoop about 1 Tablespoon of apple filling into the center of the dough and fold it in half.
Gently press the turnover on the edges to make a good connection with the egg wash. Touch the dough as little as possible to avoid heating up the butter too much.
Dip a 3 1/2-inch ring in flour and press down to glue the edges together. Cut through to make a clean line, then remove the excess. This is optional, but it will make the turnovers extra pretty.
Place the turnovers on a lined baking sheet and brush them with egg wash. Egg wash makes the dough golden and shiny when baked.
With an Exacto blade or a sharp knife, gently score a few small slits on the top of each turnover. This shouldn't cut through the dough but make a beautiful shell pattern and extra flaky layers.
Bake at 350°F for 30-35 minutes until they are flaky and golden brown.
Set the turnovers aside on a wire rack to cool completely and brush with simple syrup for extra shine (optional).