Heat oil in a large pot over medium-high heat. Season chicken with 2 teaspoon salt and add skin side down. Cook undisturbed until golden brown (about 5 minutes per side).

Add stock, water, thyme, and bay leaf. Bring to a gentle simmer over medium-high heat. Reduce heat and cook until chicken breasts reach 165°F (20–30 minutes).

Transfer chicken breasts to a cutting board. Simmer dark meat for 40 more minutes. Once done, remove both meat types from the pot and shred into bite-sized pieces.

Remove thyme and bay leaf from the broth. Add chopped onion, celery, and carrot, then simmer for 5 minutes until vegetables are tender.

Add egg noodles to the broth and cook until al dente, about 5 minutes. Stir occasionally.

Stir shredded chicken back into the pot along with pepper and adjust seasoning with the remaining salt as needed.

Serve the soup in bowls, topping with parsley and extra black pepper if desired.