Heat the oil in a large stockpot over medium heat, and add the carrots, onion, and celery. Cook for 2 minutes, then add the garlic, a pinch of salt, and pepper; stir to combine. Cook until vegetables are soft and fragrant, but not brown. If the vegetables start to caramelize, turn the heat down.
Add the herb sprigs to the pot, and stir. Pour in the broth and wine (if using), cover, and bring to a simmer. Add the chicken breast, and dunk it so it’s covered in the broth. Put the lid on, and lower heat as necessary to make sure that the broth doesn’t boil. Simmer until the chicken is cooked through, about 10 to 14 minutes.
When chicken is cooked through, carefully remove it from the soup, and set aside on a cutting board. Taste the soup at this point, and add salt to taste, if needed. Add the pasta, and turn heat to medium-high. Stir.
While the pasta cooks, shred the chicken with 2 forks. Add the chicken back into the soup, and stir. Cook until pasta is tender. Find and remove the herb sprigs from the soup before serving.