Brown the chicken. Heat oil in a pot over medium-high heat. Work in batches, brown the chicken for 2 minutes on each side. Transfer the chicken to a plate. Reserve about 2 tablespoon of grease and discard the remaining.
Add the onion then cook, stirring frequently until soft for 3 minutes. Add the garlic and stirring frequently for 1 minute. Add a small amount of broth, stirring to loosen browned bits from pan.
Add carrots, celery, bay leaf, poultry seasoning, and the remaining broth. Increase the heat and bring the broth to a boil. Lower the heat to medium, simmer, covered, until the chicken is fully cooked for 20-25 minutes.
Meanwhile, in a large bowl, add flour, baking soda, baking powder, salt, and softened butter. Mix with a fork then add buttermilk, stirring gently to combine.
Remove the fully cooked chicken from the pot. Skim the white foam and fat off the top of the water. Add frozen peas, heavy cream, and salt to the pot.
Fill a spoon with the dumpling dough and form the dough into small balls. Gently drop the dumpling balls into the pot. Cover the pot and simmer for 15 minutes without lifting the lid. While you're waiting, shred the chicken.
Once dumplings are fully cooked, put the shredded chicken back and the optional turmeric powder into the pot, stir to combine.
To thicken the soup. Add a small amount of cornstarch mixture at a time, stirring and checking until it reaches the desired consistency. Serve with chopped parsley.