1. Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion, diced carrots, and diced celery. Cook, stirring occasionally, for 5-7 minutes until the vegetables begin to soften and the onion becomes translucent.

2. Add the cut chicken pieces to the pot with the softened vegetables. Cook for 5-7 minutes, stirring occasionally, until the chicken is lightly browned on all sides.

3. Pour in the low-sodium chicken broth and water. Stir in the dried thyme, black pepper, and salt. Bring the mixture to a gentle boil, then reduce the heat to low, cover the pot, and let it simmer for 10-12 minutes, or until the chicken is cooked through.

4. Increase the heat back to medium-high and add the egg noodles or small pasta to the simmering soup. Cook according to package directions, usually 7-10 minutes, until the pasta is al dente. Stir occasionally to prevent the pasta from sticking.

5. If using frozen mixed vegetables, add them during the last 5 minutes of the pasta cooking time.

6. Taste the soup and adjust the salt and pepper if needed. Ladle the hot soup into bowls and garnish generously with fresh chopped parsley before serving.