Sift flour and salt together in a large bowl. Cut in shortening with 2 knives or a pastry blender until mixture resembles coarse crumbs.

Add cold water, 1 tablespoon at a time, tossing with a fork until the flour mixture is moistened. Wrap in plastic wrap and refrigerate for 30 minutes.

Place apples in a saucepan. Combine sugar and cinnamon; pour over apples and toss to coat. Cook covered on low heat until soft; mash with a fork to make thick applesauce.

Roll dough on a lightly floured surface to ⅛-inch thick; cut out eight 4-inch rounds with a large cookie cutter.

Place 1 heaping tablespoon of applesauce in the center of each pastry round. Moisten edges with cold water, fold in half, and press the edge with a fork to seal.

Heat oil in a deep fryer or large saucepan to 375 degrees F (190 degrees C).

Lower pies carefully into the hot oil in batches. Fry until golden brown, about 2 to 3 minutes on each side. Transfer to a paper towel-lined plate to drain.