To make the filling, heat a large skillet over medium-high heat and add the 1 teaspoon vegetable oil. When the oil is hot, add the beef and pork and cook until browned, stirring as needed, about 5 minutes. Add the onion, green onion, bell pepper, celery, salt, black pepper, and cayenne and continue to cook, stirring as needed, until the vegetables are soft, about 8 minutes. Add the garlic and cook for 2 minutes. Stir in the flour and stock, bring the mixture to a simmer, and continue cooking until it has thickened slightly, about 1 minute. Remove from the heat, stir in the hot sauce, and allow the filling to cool completely. The filling can be made up to 2 days in advance and kept, covered, in the refrigerator.

To make the dough, sift the flour, salt, and baking powder together into a medium bowl. Using a fork or pastry blender, cut the shortening into the flour mixture until it resembles coarse crumbs. In a small mixing bowl, beat the egg and milk together. Add the egg mixture to the flour mixture and stir until you have a thick but workable dough. Form the dough into a ball and flatten it into a disk. You can use it immediately or wrap it tightly in plastic wrap and refrigerate it for up to 1 day. Preheat the vegetable oil in a deep fryer to 375°F. Set a wire rack over a paper-towel lined baking sheet.

Cut the dough into 24 equal pieces. On a work surface that’s lightly dusted with flour, roll each piece out to form a 5½- to 6-inch round. Place 2 tablespoons of the meat mixture slightly off-center on a round of dough. Fold the dough over to make the edges meet, and crimp the edges with the tines of a fork to seal them. Working in batches, fry the meat pies until they are golden brown on both sides, about 3 minutes. Transfer the pies to the wire rack to drain. Serve hot.