In a very large saucepan or Dutch oven, add chicken, chicken broth, thyme, and bay leaf to cover. Turn on heat to low and let simmer for 20 minutes, until the chicken is cooked through. *Cook's Note: You'll want to poach the chicken on a low simmer and start with cold stock so the chicken cooks evenly.
Once the chicken is cooked, transfer to a 13 by 9-inch casserole dish and let cool. Reserve broth and discard the thyme and bay leaf. When chicken has cooled, shred. Use your hands or a fork and make sure to get all the meat off the bone. Discard the skin and bones.
Add flour, salt and pepper, to taste, and baking powder to a large bowl and whisk together. In a small saucepan, bring heavy cream, butter and herbs to a low simmer then add to the dry ingredients. Stir with a rubber spatula until combined. Using your hands, form dough into dumplings.
Heat a large Dutch oven over medium heat and add oil. Once oil is hot, add onions, carrots, celery and garlic. Saute until soft, 3 to 4 minutes. Add reserved broth to Dutch oven with vegetables and add the chicken. Bring to a low simmer. Add dumplings 1 at a time into the simmering soup. Cover pan with a lid and cook for 25 minutes. Add salt and pepper, to taste, if necessary.