In the bowl of a food processor, combine the flour, baking powder, and salt. Pulse for a few seconds, and then pour into a large mixing bowl.
Knead the shortening into the flour with your hands until it is crumbly. Add the milk all at once and mix in with a spatula until it begins to come together.
Turn the dough out onto a lightly floured surface. Lightly flour your hands and knead the dough ball, folding over 10 to 20 times. Using a rolling pin, roll the dough to 1/3- to 1/2-inch thickness, then cut into rounds using a 2 1/4-inch ring. Roll each round as thinly as possible, 5 to 6 inches in diameter.
Spoon 1 to 2 tablespoons of filling onto the dough, brush the edges of half of the dough lightly with the egg wash, fold over, and seal the edges together with the tines of a fork, dipping it into flour as needed. Gently press down to flatten and evenly distribute the filling. Dock pies that are going to be deep-fried, and snip or cut 3 slits in the tops of pies that will be baked or pan-fried.
To pan-fry pies: Place a medium saute pan over medium-low heat along with 1 to 2 tablespoons vegetable oil, canola oil, or butter. Once heated, place 2 to 3 pies at a time into the pan and saute until golden on both sides, 3 to 4 minutes per side. Allow to cool 4 to 5 minutes before serving.
To deep-fry pies: Heat vegetable oil in a deep-fryer or a large heavy pot to 375ºF. Once hot, add 1 to 2 pies at a time and fry until golden brown, 3 to 4 minutes.
To bake pies: Heat the oven to 350ºF. Place finished pies on an ungreased half-sheet pan and bake until golden brown, 25 to 30 minutes.