Preheat the oven to 350° F.
Place the whole chicken in a large 4-6 quart baking dish. Pour in water until the chicken is about half covered. Season well with salt and pepper. Cover with tinfoil and bake 25 minutes for each pound, or until internal temperature reaches 165° F. So, if your chicken weighs 3 pounds, bake for about 1 hour and 15 minutes.
Once done, remove the chicken from the baking dish and let cool enough to handle, then remove meat from bones and shred. While chicken is cooling, strain the liquid from the baking dish into a large bowl. Measure how many cups you have and set aside.
Add oil, celery, carrots, and onion to a 6-quart or larger dutch oven or stockpot. Cover and cook on medium-high heat for about 10 minutes, stirring occasionally, until vegetables are slightly tender.
Sprinkle the flour over the vegetables and mix to combine. Let cook for one minute, then gradually add the liquid from the chicken, whisking to combine. Add enough extra chicken broth to make a total of 10 cups of liquid in the pot. Add chicken bouillon, salt, pepper, and thyme to the pot, and stir to combine. Bring to a boil, stirring occasionally. Then reduce heat to medium-low, cover, and let simmer for 30 minutes.
While soup is simmering, make the dumpling batter. In a medium bowl, mix together flour, baking powder, salt, and pepper. In a small bowl, whisk together buttermilk, egg, and parsley (if desired). Pour wet ingredients into dry ingredients and mix until combined. Do not over mix dumplings or they will become dense.
After soup has simmered for 30 minutes, add shredded chicken and peas to pot and stir to combine.
Using a spoon, gently drop dumpling batter into the soup to create about 8-10 dumplings. Don’t make them too large, as the dumplings will double in size as they cook. Cover and simmer over medium heat for 18-20 minutes, or until dumplings are cooked through. Do not remove the lid while the dumplings are cooking, as they need the steam to cook properly. To make sure dumplings are cooked through, cut one in half. If not, cover and cook for an additional 2-3 minutes.
Serve warm & enjoy!