Place the water, carrots, celery, onion, and bay leaf in a 6-quart or larger slow cooker and stir to combine; set aside. Place the measured salt, measured pepper, and thyme in a small bowl and stir to combine; set aside. Place the chicken on a work surface or cutting board and pat it dry with paper towels. Cut off and discard any extra fat hanging around the body cavity. Drizzle the oil on the chicken and rub it all over the skin. Season inside and out with the thyme mixture. Place the chicken on top of the vegetables in the slow cooker. Cover and cook until the chicken is cooked through and falling off the bones, about 6 hours on high or 8 hours on low. Transfer the chicken to a rimmed baking sheet. When it’s cool enough to handle but still warm, use your hands to shred the meat into bite-sized pieces (discard the skin, cartilage, and bones). Return the shredded chicken to the slow cooker and add the parsley. Add the rice or noodles, if using, and stir to combine. Taste and season with salt and pepper as needed.