Make the stock: Clean and quarter chicken, then season with salt and black pepper. To a large stockpot, add celery, garlic, onion, carrots, peppercorns, bay leaves, and butter. Add a teaspoon each of salt and pepper and sauté for 5 to 10 minutes, until vegetables soften.
Add chicken pieces to pot and cook for 5 to 10 minutes, stirring occasionally, until meat slightly browns. Next, add 1 gallon water and simmer over medium heat for about 45 minutes, until chicken begins to fall off the bone.
While chicken simmers, make the dumplings: In a large mixing bowl, combine 4 cups flour with a pinch of salt. Add lard and mix thoroughly with your hands. At this stage, the dough should form a very crumbly ball.
Add ice water 2 cups at a time, making sure not to add ice. Using your hands, continue to mix dumplings. At this stage, the dough should be a bit sticky but not too wet, like the consistency of pie dough. If it's too dry, add a bit of water; if it's too wet, add a bit of flour. Form dough into 3- to 4-inch balls.
When chicken is done, remove and reserve meat and strain liquid back into stockpot. Remove all vegetables and season to taste with salt, black pepper, poultry seasoning, granulated garlic, and white pepper. Bring stock to a boil.
Using floured rolling pin, roll out dumplings on a floured surface until almost paper-thin. Using a pizza cutter, cut dumplings into small squares. Using metal spatula, lower dumplings into boiling stock in batches, stirring stock with a wooden spoon after each addition. (If dumplings are too sticky, sprinkle them with flour.) After all dumplings have been added, boil stock for about 5 minutes, until it thickens. Pull chicken from bones and return meat to pot. Let rest about 5 minutes before serving.