Prepare the pastry: In a large bowl, sift together the flour and salt. Cut in the chilled shortening using two knives or a pastry blender until the mixture looks like coarse crumbs.
Add water gradually: Stir in cold water, 1 tablespoon at a time, using a fork to mix until the dough starts to hold together. Be careful not to add too much water—the dough should form a ball when squeezed. Wrap it in plastic wrap and refrigerate for about 30 minutes.
Make the apple filling: In a saucepan, add the diced apples. Mix the brown sugar, cinnamon, and nutmeg, then pour this mixture over the apples and toss to coat. Cook over low heat, covered, until the apples soften. Mash them into a thick applesauce-like consistency, then set aside to cool.
Roll out the dough: On a lightly floured surface, roll out the chilled dough until it’s about ⅛-inch thick. Use a large cookie cutter to cut out eight 4-inch rounds.
Assemble the pies: Place a heaping tablespoon of the apple filling in the center of each dough round. Moisten the edges with a little cold water, fold the dough over to form a half-moon shape, and press the edges together with a fork to seal. Repeat this process for the remaining dough and filling.
Heat the oil: In a deep fryer or large saucepan, heat the oil to 375°F (190°C).
Fry the pies: Carefully lower the pies into the hot oil in batches. Fry each pie for about 2 to 3 minutes on each side, until golden brown. Once cooked, transfer them to a plate lined with paper towels to drain excess oil. Repeat with the remaining pies.
Enjoy your delicious fried apple pies!