In a large pot over medium-heat, add the chicken breasts and stock just until the chicken is covered and fully submerged in liquid. Season with a little salt and pepper. All remaining chicken stock can be kept aside and reserved for later.
Bring stock to a low boil and then reduce heat to a simmer, with very few gentle bubbles visible. Allow the chicken to simmer for approximately one hour, or until the meat shreds apart at the pull of a fork. Remove from the stock to let cool. Reserve the stock for later. Shred the chicken off the bone with a fork and set aside.
To Prepare the Soup
Heat a large soup pot or dutch oven over medium-heat. Coat the bottom of the pan with a drizzle of olive oil. Add the onion, carrots, and celery. Saute until fragrant and beginning to soften, about 8 minutes. Add the garlic and saute for 2 minutes more, or until fragrant. Season with salt and pepper.
Add the rosemary and saute for 2 minutes more. There should be a small bit of browning developing on the bottom of the pan, this is called "fond." Add the white cooking wine, and using a wooden spoon, scrape the bottom of the pan to release the fond. Allow the wine to cook down for 2-3 minutes.
To the pot, add the stock that was used to cook the chicken previosuly. If there is any skin or bones in the stock leftover from cooking the chicken, just pour the stock into the pot through a strainer/collander. Add the additional stock that has not been used yet.
To the soup, add the shredded chicken, kale, peas, and fresh lemon juice. Turn heat to low and allow the soup to simmer.
While soup is simmering, prepare your pasta. Make sure to cook the pasta just to al dente so that it's not soggy. Once done, add the pasta to the soup.
Top the soup with freshly chopped parsley, and any more salt and pepper, as needed. You can also add additional chicken stock if you prefer the taste of a thinner soup. Enjoy!