Whisk together flour, salt, and cinnamon for crust. Cut in shortening until very crumbly. Sprinkle enough water over the mixture to just hold the dry ingredients together; mix together and form into a ball. Wrap with waxed paper and chill in the refrigerator for 20 minutes.
Roll dough on a lightly floured surface (1/2 batch at a time) to a 1/8-inch thickness. Cut into six 7-inch squares. Reserve any extra dough for decorative garnish, if desired.
Place one apple in the center of each square of dough.
Combine brown sugar, cinnamon, nutmeg, and cloves in a small bowl. Divide mixture evenly between the apple cores and dot the top of each apple with 1 teaspoon butter. Bring the opposite corners of each square together at the top of each apple, pressing gently to seal the seams. Transfer to a large baking dish, making sure the dumplings do not touch.
Preheat the oven to 500 degrees F (260 degrees C).
Combine water, sugar, corn syrup, butter, cinnamon, and nutmeg for syrup in a pan and bring to a boil. Allow to boil for 3 minutes. Pour syrup mixture over the top of all of the dumplings.
Bake immediately in the preheated oven until the crust begins to turn light golden brown, 5 to 7 minutes. Reduce the oven temperature to 350 degrees F (175 degrees C) and bake, occasionally spooning hot syrup from the bottom of the pan over the top of the dumplings, until apples are tender, 30 to 35 more minutes.