Make the filling: In a large cast-iron skillet over medium-low heat, melt the butter. When the foam begins to subside, stir in the granulated sugar, cinnamon, ginger (if using), and salt. Add the apples and cook, stirring frequently, until they are very tender and most of the liquid has evaporated, 25–30 minutes. Transfer to a large rimmed baking sheet and set aside to cool to room temperature while you prepare the crust. (If you leave the apples in the cast iron, they may discolor.)
Make the crust: In a large bowl, add the shortening, flour, salt, granulated sugar, and baking powder. Using a pastry blender or fork, cut the fat into the dry ingredients. In a medium bowl, whisk together the egg yolk and milk, then pour into the flour mixture. Still using the pastry blender, work the wet ingredients into the flour mixture just until a shaggy dough comes together, then press into a 2-inch-thick disk and refrigerate for at least 20 minutes and up to overnight.
Line a large baking sheet with parchment paper and set aside. Fill a small bowl with cold water and set by your work surface. Lightly flour a clean work surface and a rolling pin, then retrieve the dough from the fridge and cut into two equal pieces. Return one piece to the fridge and place the second one on your work surface. Roll the dough out to an even sheet, just barely ⅛ inch thick, lightly flouring the dough as needed to prevent sticking. Using a 3¾-inch biscuit cutter, punch circles from the dough, setting the scraps aside.
Assemble the pies one at a time for the best results: Brush the outer edge of one circle lightly with water, then place 3 tablespoons (about 2 ounces) of the apple filling in a neat bundle at the center of the circle. Fold the dough tightly in half over the filling, gently pressing any air out of the pocket as you fold. Pinch the edges to seal, place the pie on the prepared baking sheet, and gently crimp the edges with the tines of a fork. Continue rolling, cutting, and shaping the remaining piece of dough in this manner, then press the scraps from both sheets together and reroll only once. Refrigerate the pies for at least 20 minutes and up to 3 hours (or wrap tightly in plastic wrap and freeze for up to 3 months).
When you are ready to fry the pies, in a large, heavy pot, add enough oil to reach 2½ inches up the sides of the pot. Heat until the oil registers 350°F on a deep-fry thermometer. Line a second baking sheet or a large heat-resistant platter with paper towels and set by the stove.
Working in batches, fry the pies, turning occasionally and maintaining an oil temperature between 330°F and 360°F, until evenly golden brown and cooked through, 3–4 minutes. Using a a slotted spoon, transfer to the prepared baking sheet to drain. Let the pies cool slightly, then dust with confectioners’ sugar and serve warm or at room temperature.