How to Make It
Bring a small saucepan of water to a boil. Make a small, shallow X in the bottom of each peach, just to break the skin. Place each peach in the boiling water for 10 seconds; immediately plunge into a bowl of ice water. Peel the skin with a paring knife. Remove the pits, and cut the peaches into slices.
Place the peach slices, sugar, lemon juice, and cardamom in a saucepan. Bring to a boil over high; reduce heat to low. Cover and simmer 5 minutes. Stir together cornstarch and water; stir into simmering peach mixture. Increase heat to high, and bring to a boil; boil until thickened, about 1 minute. Remove from heat, and stir in butter. Transfer to a bowl, and chill until ready to use.
Sprinkle a work surface with flour. Generously flour both sides of biscuits, and roll each into a 5 1/2-inch circle (about 1/8 inch thick). Place a heaping tablespoon of the chilled filling in the center of each dough circle, leaving a 1-inch border around the edge. Do not overfill. Using a brush or your finger, dampen the edge of the circle with water. Carefully fold the dough in half, pressing the edges together to make a half-moon shape. Press edges with a fork to seal.
Melt shortening in a Dutch oven over medium; heat to 325°F. Fry pies, in batches, until deep golden brown, 4 to 5 minutes on each side, turning as necessary to ensure even browning. Remove and drain on paper towels; if desired, dust with powdered sugar.