Chicken and Dumplings is comfort food in a bowl with flavorful homemade chicken soup and large, plump dumplings.
Place the chicken in an 8-quart Dutch oven, or a large, heavy-duty pot with a cover.
Add the water, carrot, celery, onion, thyme, and bay leaf to the chicken. Bring to a boil (uncovered).
After the mixture has come to a boil, cover the Dutch oven, reduce heat to low, and let simmer for 1 hour.
Remove the chicken from the Dutch oven and transfer to a large bowl. Set the chicken aside to cool.
Increase the heat and bring the stock to a simmer.
Skim off, and reserve in a bowl, as much chicken fat as you can that is at the top of the stock.
In a small bowl, mix the 2 tablespoons flour with 2-3 tablespoons of the reserved chicken fat to make a paste. (Add more flour if needed.)
Add the fat and flour paste to the stock. Reduce heat and simmer for 15 minutes.
After the 15 minutes, remove the skin from the chicken and shred it with forks. Add the shredded chicken to the stock.
Add salt, black pepper, cayenne pepper, and chicken bouillon. Remove the bay leaf, and continue to simmer for 10-15 minutes as you prepare the dumplings.
In a large bowl, whisk together the sour cream, milk, thyme leaves, and eggs. Set aside.
In a medium bowl, whisk together the flour, baking powder, and salt.
Add the flour mixture to the sour cream mixture. Stir until just incorporated; do not overmix.
Using a 1/4-cup scoop, scoop large dollops of the dumpling mixture on top of the simmering chicken stock.
Increase to medium-high heat, cover, and simmer for 10-15 minutes, or the dumplings are light and fluffy. (To check for doneness, an inserted toothpick should come out clean.)
Serve immediately, garnished with extra thyme sprigs (optional).