Prepare the Soup Base: Place the broth, water, chicken, salt, pepper, and bay leaf in a large soup pot or Dutch oven over medium-high heat. Bring the mixture to a boil, then lower the heat to medium-low and let it simmer gently for about 25 minutes. Skim off any foam that forms on the surface. Check that the chicken is fully cooked by ensuring it reaches an internal temperature of 165°F for thighs or 155°F for breasts.
Cook the Vegetables: While the soup base is simmering, heat the oil in a skillet over medium heat. Add the chopped onion, celery, and carrots, and sauté for 6–8 minutes, stirring occasionally, until they soften and develop a light golden color. Once cooked, transfer the vegetables into the soup pot.
Shred the Chicken: After the chicken is cooked, remove it from the pot and allow it to cool slightly. Once cool enough to handle, shred the meat into small pieces, discarding any skin or bones.
Add the Pasta: Stir the pasta into the soup pot and cook for 5 minutes, or until the pasta is just tender. Add the shredded chicken back to the pot and continue cooking for another 5 minutes, ensuring the pasta is fully cooked but not overdone.
Finish the Soup: Mix in the parsley, dill, and garlic. Taste the soup and adjust the seasoning as needed by adding more salt or pepper. Remove and discard the bay leaf before serving.
Storage Instructions: Allow any leftovers to cool before storing them in an airtight container in the refrigerator. The soup will stay fresh for up to 4 days.