Cover the dried apricots with water in a saucepan and simmer until soft, about 1 hour.
Mash well with a potato masher and add the sugar and spices. Set aside to cool.
Pastry
Sift together the flour, salt, and sugar.
Cut in the shortening with a pastry blender or two knives and gently combine till the mixture resembles cornmeal or tiny peas.
Sprinkle water over the mixture, a tablespoon at a time, and mix with a fork, using only enough water to allow the pastry to hold together when pressed gently into a ball.
Roll out dough to ⅛ inch to ¼ inch in thickness.
Using the bottom of a coffee can (or a 6-inch baking form), cut the dough into rounds and place 3 to 4 tablespoons of the filling on one half of each round.
Moisten edges of the dough round with water, and pull the uncovered half over the filling, pressing together to seal.
Use fork tines or your fingers to crimp edges of the dough.
Heat an inch of vegetable oil to 350 degrees and fry each pie until golden brown, about 3 minutes.
Notes
Adapted from The Texas Cowboy Kitchen, by Grady Spears and June Naylor. Published by Andrews McMeel Publishing.