Whisk the flour, baking powder, and 1 teaspoon of the salt together in a medium mixing bowl. Rub the shortening into the flour mixture using your fingertips until it resembles coarse crumbs. Add the milk, 2 tablespoons at a time, just until you have a rough ball of workable dough. Knead the dough 3 to 4 times, until it is mostly smooth, but do not overwork.
Divide the dough into 2 equal pieces. Roll out each piece of dough, using a floured rolling pin, to a sheet about 1/16-inch thick, on a floured piece of waxed paper or parchment paper. Cover the dough, still on the waxed paper or parchment, with a tea towel, and dry for at least 8 hours. This can be done the night before or early in the morning.
Two to three hours before the dumplings are ready to cook, put the chicken, water, and the remaining tablespoon of salt in a 7-quart pressure cooker. Do not fill above the cooker's "maximum fill" line, or two-thirds full. Cover and lock the lid. Bring to pressure over high heat, about 20 minutes. Reduce the heat to low, so that you barely hear hissing from the pot. Cook for 45 minutes.
Release the pressure using the cooker's release device (read the manual!) or cool the cooker by running cold water over the lid for 5 minutes. Open carefully. Remove the chicken from the broth and set aside to cool. The meat should be tender and falling away from the bone. Once the hen is cool enough to handle, pull the meat from the bones in small pieces, cover and set aside. Discard the skin and bones.
Set a cheesecloth-lined colander in a large container and pour in the broth, discarding the solids. Taste and season the broth with additional salt, if needed. Return the broth to the pressure cooker, cover and bring to a boil over high heat. Reduce the heat to medium to maintain a gentle boil.
Cut the dough into 1/2-inch-wide strips, break into 1 1/2-inch long pieces, and drop into the boiling broth. When all the dough has been used, gently push all of the dumplings down into the broth with a slotted spoon. Do not stir the dumplings. Cook the dumplings until they are cooked through, but not falling apart, about 10 minutes. Turn off the heat and add the meat. Serve in bowls with freshly ground black pepper.