Preheat oven to 350°F. On a rimmed baking sheet lined with parchment paper, lay the chicken breasts skin side up. Rub them all over with oil and sprinkle salt and pepper on them. Place into oven and roast for 35-40, until done. Remove from the oven and let cool until you can handle them. Remove the skin, pull the chicken off the bones and shred it into bite-sized pieces using your hands or two forks. Cover and set aside.
While the chicken is cooling, heat two tablespoons of oil in a 5-quart dutch oven or soup pot over medium heat. Add the onions and celery to the pot and let cook until softened, about 5-6 minutes. Stir in the flour and let cook for 1 minute.
Pour in the chicken stock and water. Add the potatoes, carrots, thyme, bay leaf and sea salt to the pot and stir. Bring to a boil, reduce heat to medium-low and let simmer uncovered until potatoes and carrots are tender, about 20 minutes. Remove the bay leaf. Stir in the chicken, let heat through (about 2 minutes), then add fresh parsley and serve.