2/3 cups buttermilk (I often sub with watered down plain yogurt)
2 tablespoons chopped fresh parsley
Make the Soup-Pat the chicken dry with paper towels and season generously with salt and pepper. In a large Dutch oven, heat 2 tablespoons of the oil over medium-high heat. Working in two batches, brown the chicken until golden, about 4 minutes per side. If the pot is looking a little dark on the bottom, splash some water and scrape up any browned bits between batches, and keep those juices with the chicken.
Return all the chicken to the pot and add 8 cups water, the bay leaf, thyme, rosemary, and 1 tablespoon salt. Bring to a boil, reduce the heat to a gentle simmer, and cook for 1 hour.
Strain the broth through a colander set over a large bowl (there should be about 8 cups liquid; skim off some of the fat if you want). Discard the bay leaf and herb sprigs. Using two forks or a pair of tongs, pick the chicken meat off the bones (discard the bones and skin and set aside).
In the same Dutch oven, heat the remaining 2 tablespoons oil and the butter over medium-high heat. Add the onion, carrots, and celery and cook, stirring, until the carrots begin to soften, about 6 minutes. Add the flour and cook, stirring, until all the flour has been absorbed and darkens a bit, about 5 minutes. Add the strained broth, the chicken meat, and the potato, bring to a boil, then reduce the heat and simmer until the broth thickens, about 20 minutes. Stir in the cream, if using. Season to taste with salt and pepper.
While the broth simmers, make the dumpling dough In bowl, whisk together flour, cornmeal, baking powder, baking soda and salt. Using pastry blender, cut in butter until in coarse crumbs. Stir in buttermilk and parsley to make sticky spoonable dough.
Drop by 8 spoonfuls onto simmering stew. Cook, covered and without lifting lid, until dumplings are no longer doughy underneath
Divide the soup and dumplings among bowls. Garnish with parsley.