Wash the stomachs in cold water until completely clean.
Preheat the oven to 350℉/177℃.
Wash and dice the potatoes, onion, celery, and smoked sausage.
Combine the sausages, cubed potatoes, chopped onions, celery, and parsley. Season with salt and pepper to taste. Then add the sliced smoked sausages and mix thoroughly.
Use a toothpick or cooking twine to close the one open end of the pigs' stomachs, leaving a large opening for stuffing. Sew up any tears.
Stuff sausage mixture into the stomachs, pressing well with each addition; the stomach will stretch as you fill it up. Once stuffed, close the other end of the stomach using the same process. (Pig stomach might be longer than needed, feel free to cut it off where needed.)
Place both stuffed stomachs in a roasting pan. Pour a little water into the pan. Cover with foil and bake for 2½-3 hours, basting about every 20 minutes with water or pan juices. Occasionally check to make sure there's still some liquid in the pan. If not, add some.
Remove the foil during the final 30 minutes, and continue to cook until the stomachs are golden brown.
Remove stuffed stomachs from the roasting pan, take off the toothpick or twine, and place hog maws on a serving plate. Slice them into 1-inch thick slices or scoop the filling out.