In a small-medium pan, heat chopped apple pieces, sugar, lemon juice, and cinnamon over high heat and bring to a boil. When it boils, reduce heat to low and cover. Simmer for 5 minutes.
In a tiny bowl, stir together cornstarch and water and then add into apple mixture.
Increase heat and bring to a boil again. Boil until mixture is thickened (takes about 1 minute). Remove from heat and add in butter.
Put mixture into a heat-safe bowl and set aside. Refrigerate so that you can work with the mixture more easily in the next steps.
On waxed paper, sprinkle flour to prevent dough from sticking.Flour each side of a biscuit and roll out/flatten into a thin circle. Circle will be almost 6 inches wide. Spoon 2 tablespoons of the filling in the center of the circle and leave a border around the edge to be able to close the pie. If you add too much filling, it will make it hard to seal the edges of the pies.
Fold the circle to create a half-circle. To seal the edges together, dip a small brush or your finger in a bit of water and go around the edges of the dough with the water. The water and dough combination will act as a glue to keep the edges together. Press with the tines of a fork to seal and create the lined edges of the pie.
To fry the pies, melt shortening in a Dutch oven. To test if the temperature is high enough, sprinkle a drop of water in to see if it sizzles. If it does, the oil is hot enough. A candy thermometer would read about 325 degrees (F). It should not be so hot that it smokes. If smoke begins, turn off heat and remove pot from heat. Add 2-3 pies to Dutch oven and fry for 4-5 minutes on each side. The pies will be golden brown when done.Have a plate lined with paper towels ready for when you remove the pies. Place pies on the plate with paper towels to absorb oil.Top with sprinkled powder sugar.