Cut a 3-inch section of the carrot and set aside. Chop the remaining carrot into small cubes. Cut a 4-inch piece of celery stalk and set aside with the carrot. Chop the remaining celery into small cubes.

Place the chicken, breast facing up, in a large pot. Toss the ¼ carrot, 4-inch piece of celery, onion top, smashed garlic clove, bay leaves, peppercorns, and 1 tablespoon of salt around the chicken.

Pour in 12 to 14 cups of water, depending on the size of your pot.

Cover the pot with a lid, turn the heat to medium-high, and bring to a simmer.

Cook at a gentle simmer for 50 minutes.

After 50 minutes, the broth will be aromatic, and the chicken will be cooked through.

Carefully transfer the chicken to a plate and allow it to cool.

Strain the broth and pour it back into the pot. Add the thyme, chopped carrots, and chopped celery.

When cool enough to handle, shred the chicken by hand, removing bones and skin.

Melt the butter. In a medium bowl, stir flour, pepper, salt, parsley, milk, and melted butter until mixed.

Remove the thyme from the soup.

Stir the shredded chicken and any juices into the soup.

Bring the broth to a gentle simmer and scoop portions of the batter into the soup.

Cover with a lid and cook the dumplings at a low simmer for 5 to 7 minutes.

Once turned over, simmer with the lid on for another 8 to 10 minutes.