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 flour mixture is moistened. When squeezed, a handful of the mixture should form a ball. Wrap in plastic wrap and refrigerate for 30 minutes.

Place diced 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. Set aside to cool.

Roll dough on a lightly floured surface to 1/8-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 pastry edges with water, fold in half, and seal the edges by pressing with a fork.

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