Heat the oil in a large dutch oven.
Season the chicken with salt and pepper.
Brown the chicken about 4 to 6 minutes per side.
Transfer the chicken to a plate for later.
Add the chopped celery, onions, thyme and garlic to the drippings in the dutch oven and cook until the vegetables are soft. This will take about 5 to 7 minutes.
Add 8 cups of water and 2 cups of chicken stock in with the vegetables.
Shred the chicken with a fork (discard the bones and skin) and add it back to the dutch oven. Add the bay leaves too.
Bring the mixture to a simmer and cook about another 20 to 30 minutes until the chicken is fully cooked.
While that is simmering, whisk together a 1/2 cup of flour and 2 cups of the cooking liquid to create a thickening sauce. Slowly mix a little bit of this paste back in the pot a tablespoon at a time until it all dissolves. The soup mixture will thicken in about 8 to 10 minutes.
Next you will make the dumplings.
In a separate bowl, mix the remaining 2 cups of flour, baking powder, baking soda, salt, pepper and parsley. Then add the melted butter and buttermilk to the dry mixture and stir. The dough will get a bit thick.
Finally, spoon out small portions of the dough into the broth mix in the dutch oven. I evenly distributed about 8 to 10 spoonfuls. Simmer another 12 to 15 minutes until the dumplings are firm. Serve warm.