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Add the mix to a large skillet and cook over medium heat, stirring regularly to prevent scorching. When the apples are soft, pour the mix into a cake pan, press plastic wrap against the apples and cool in the fridge. The pies are easiest to fill when the apples are very cold.
For the dough: In a stand mixer fitted with a paddle attachment, combine the flour, butter, sugar and salt. Mix on the lowest speed until there are almost no large chunks of butter remaining. Be careful not to over mix, the dough should be crumbly. Add the lard and continue to mix until all the butter and lard pieces are pea size.
Whisk together the egg and cold water and slowly stream the liquid into the mixer running on low speed. Once the dough comes together, stop mixing. Wrap the dough in plastic wrap and rest it in the refrigerator for 30 minutes.
Roll the dough out on a floured surface to about 1/8-inch thick. Cut out four to six 6-inch circles and lay them on a lightly floured counter. Brush the top of each pie circle with some egg wash.
Place a hearty spoonful of filling in the center of each pie circle. Fold the circles to half-moon shapes and pinch them shut. Be sure to pinch tightly and seal the whole pie so it doesn't burst in the fryer later. Pies can be frozen at this step for later use.
Preheat the deep fryer to 350 degrees F.
Fry the pies until golden brown, 4 to 5 minutes if fresh or about 7 if they are frozen, and serve hot.