In a 12-quart stockpot, add your hen, onion, celery, and broth and cook over medium-low heat for 2-3 hours or until vegetables are tender.
Let cool and then remove hen and vegetables from broth.
Discard the vegetables and debone the hen, making sure to remove the skin as well.
Set hen meat aside.
Once ready to make the dumplings, create a clean, wide workspace on your countertop.
Place a layer of flour around your workspace and add ½ cup in a small pile in the middle.
Place another 1 cup of flour in a glass bowl and set aside.
Making sure your stock is hot (but not too hot to handle), skim off the top layer of fat using a ladle and place in a bowl.
Once settled, this should result in about 4-5 cups of liquid in the bowl with about 1 inch of golden, clarified fat floating on top. Quickly whisk the stock so that the fat becomes incorporated and pour 1 cup of the emulsified liquid into the bowl with the flour. The fat becomes separated from the stock rather quickly, so this is a job best for 2 people.
As one person pours in the liquid, the other can use their hands to combine the ingredients until the mixture forms a paste.
Add more liquid as necessary until all the flour is incorporated.
Scoop the paste into the pile of flour on your workspace and knead it into a soft dough (roughly 6-8 times).
Using a floured rolling pin, roll out the dough until it is nearly transparent and about 1/8-inch thick.
Cut dough into ½ x 2 inch strips and use a spatula to transfer to a parchment-lined cookie sheet.
Keep repeating this process until you have used up the bowl of stock, and be sure to add additional sheets of parchment paper between layers of dough.
To prepare the dish, bring the remaining stock to a boil and salt to taste.
Add the strips of dough one-by-one to the stockpot and stir frequently to keep them from sticking to the bottom of the pot or each other.
Add in hen meat and stir to combine.
Turn heat down to medium and simmer for 30 minutes or until the dumplings are cooked through and plump, stirring frequently the entire time.
Add additional broth as needed, and salt and pepper to taste.
Serve within 2 hours of cooking and enjoy!