Heat 2 tablespoons of olive oil in a large stockpot or Dutch oven over medium-high heat. Season the chicken pieces with salt and pepper. Add chicken to the pot and cook until lightly browned on all sides and cooked through, about 5-7 minutes. Remove chicken from the pot and set aside.

In the same pot, reduce heat to medium. Add the remaining 2 tablespoons of olive oil. Add chopped onion, carrots, and celery. Sauté for 8-10 minutes, or until vegetables begin to soften. Add minced garlic and cook for another 1 minute until fragrant.

Pour in the chicken broth and water (if using). Add the bay leaf, dried thyme, and crushed rosemary. Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 15 minutes to allow flavors to meld.

Increase heat to medium-high and bring the soup back to a rolling boil. Add the egg noodles and cook according to package directions, usually 7-10 minutes, or until al dente. Add the cooked chicken back into the pot during the last 2-3 minutes of noodle cooking.

Remove the bay leaf. Taste the soup and season with additional salt and pepper as needed. Stir in the fresh chopped parsley just before serving.

Ladle the hot soup into bowls and serve immediately.