Heat the olive oil in a large pot over medium heat. Add the chicken thighs (or breasts) and sear for 3–4 minutes, until lightly browned on one side. Flip and sear the other side for another 2–3 minutes. Remove the chicken to a plate and set aside.
In the same pot, add the onion, carrot, and celery. Sauté for about 5 minutes until the vegetables begin to soften and the edges become slightly translucent. Add the garlic and cook for another 30 seconds, until fragrant.
Pour in the chicken stock and water, then scrape up any browned bits from the bottom of the pot. Return the chicken to the pot, add the bay leaf and thyme, and season with a pinch of salt.
Bring the mixture to a gentle simmer. Reduce the heat to maintain a steady simmer and cook for 20–25 minutes, until the chicken is cooked through and tender.
Remove the chicken to a cutting board. Once cool enough to handle, shred or chop the meat into bite-sized pieces and discard the bones if you used bone-in thighs.
Return the shredded chicken to the pot. Increase the heat slightly and bring the broth to a simmer. Add the egg noodles and cook according to package directions, usually 6–8 minutes, until al dente.
Taste and adjust salt and pepper as needed. If you like a brighter finish, stir in a little chopped parsley just before serving.
Ladle into bowls and serve hot. This soup stores well in the refrigerator for up to 3 days and can be frozen for longer storage, though noodles may soften a bit after freezing.