Preheat the oven to 350 degrees.
Get the pie dough out of the fridge and roll it out on the generously floured countertop into a 15"x15" square. Use a ruler to cut off the extra 1" of ragged edges around the outside of the square so you're left with a perfect 14"x14" square. Then, cut four 7"x7" squares to wrap the apples in. Save the scraps to cut leaves out of if you'd like to decorate the tops of the apple dumplings.
Take each apple and place it in the middle of the square of pie dough. Fill the cored center of each apple with the cinnamon sugar filling leaving space to place the small square of butter on top. Fold the edges of the square up over the top of the apple bringing them all to the center. Pinch all 4 corners of the pie dough together. If the dough won't hold, you can dip your finger in the egg wash to help seal it.
Place all 4 dumplings in the pan, make sure they aren't touching. Decorate the tops of the dumplings with leaves. Egg wash each dumpling and sprinkle the leftover cinnamon sugar over the tops of them.
Stir the Brown Sugar Syrup one more time and then pour it into the bottom of the pan. The pan does not need to be greased because of the butter in this Brown Sugar Syrup.
Place the Apple Dumplings in the oven and bake at 350 degrees for 1 hour.
Once they are a nice golden brown color, remove them from the oven and let them cool in the 9"x13" pan until they are just warm.
Serve with the Brown Sugar Syrup spooned over the top of each dumpling, and maybe with a scoop of vanilla ice cream, and enjoy!