Prepare your favorite double pie crust dough and keep it refrigerated.
Preheat oven to 350°F (175°C).
In a 10-inch cast iron skillet, add water until it is about 1 1/4 inches deep. Stir in the 1 1/4 cups of brown sugar.
Place the skillet on the stove over medium-low heat and slowly bring the syrup to a gentle boil.
Peel, core, and slice the apples. (If large, cut slices in half).
Roll the chilled pie crust dough out to 1/8-inch thickness. Cut into 4 1/2-inch squares.
Place 4 to 5 apple slices in the center of each square. Top with 1 tbsp granulated sugar, a light dusting of cinnamon, and a chopped pat of butter.
Bring the corners of the dough up to the center and pinch the seams tightly to seal the pouch. Repeat until 6-8 dumplings are formed.
Once the syrup is boiling, gently place the dumplings into the skillet. Drop any extra apple slices between the dumplings into the syrup. Let sit on medium heat for 3 minutes.
Carefully transfer the hot skillet into the preheated 350°F oven.
Bake until the dumplings are golden brown and the syrup is bubbling thick (approx. 35-50 minutes).
Remove from oven and let cool until very warm before serving.