Cook the apples with the water in a covered pot over medium-low heat for about 1 hour, or until all liquid has been absorbed. Stir occasionally. Add the sugar, butter and cinnamon, mixing well; set aside to cool. Unfold the pie crust and break into 8 equal pieces like pie slices. Place 1 heaping tablespoon of fruit on each round of dough, leaving a 1/2-inch border all around. Dip your finger in water and moisten the edges of the crust, then place a second round on top of the filling and press the edges of the crust, then place a second round on top of the filling and press the edges to seal. Dip the tines of a dinner fork in flour and crimp the edges to ensure a proper seal.
Pour the oil into a cast-iron skillet to a depth of a little less than 1/2 inch. (This would be 11/2 cups oil in a 10-inch skillet.) Heat over medium-high heat. When the oil is hot, place 3 to 4 pies in the skillet and cook for about 2 minutes on each side, or until golden brown. Drain on paper towels. Repeat until all the pies are cooked, or wrap and freeze some of the uncooked pies for another day.
Sprinkle the pies with granulated sugar while they're hot.