01 - Heat olive oil in a large pot or Dutch oven over medium heat. Add the onion, carrots, and celery; sauté for 6–7 minutes until softened. Add garlic and cook for 1 minute. Place chicken pieces into the pot, then pour in chicken broth. Add bay leaf, dried thyme, dried parsley, salt, and pepper. Bring to a boil, then reduce to a simmer. Cover and cook for 30–40 minutes, until chicken is cooked through and tender.
02 - On a clean surface, mound the flour and sprinkle with salt. Make a well in the center; add eggs. Using a fork, beat eggs, gradually incorporating flour. Add water a little at a time if needed, until a shaggy dough forms. Knead by hand for 5–7 minutes until smooth and elastic. Wrap in plastic and let rest for 20 minutes.
03 - Remove cooked chicken from the soup and let cool slightly. Discard bay leaf. Shred chicken into bite-sized pieces, discarding bones.
04 - Divide rested dough into two portions. On a floured surface, roll each portion to 1/8-inch thickness. Cut into 1/4-inch wide strips, about 3–4 inches long. Dust lightly with flour to prevent sticking.
05 - Bring the soup to a gentle boil. Add egg noodles and cook for 5–7 minutes, stirring occasionally, until noodles are tender. Return shredded chicken to the pot and heat through for 2–3 minutes. Taste and adjust seasoning if necessary.
06 - Ladle soup into bowls, garnish with fresh parsley, and serve hot.