Place bone-in chicken breasts in a large pot. Pour 8 cups of water over the chicken breasts and make sure that the chicken is fully submerged in the water. Add 2 celery stalks, 1 carrot (halved), 1/2 yellow onion, garlic, peppercorns, and salt. Bring the pot to a boil, then reduce heat and lightly simmering for about 2 hours.
Once simmered, use tongs to gently remove the chicken and place it on a large cutting board. Allow the chicken to cool so that you can handle it with your hands.
Meanwhile, set a strainer over a separate large bowl or pot. Gently pour the broth into the strainer and use a spatula to press down on the vegetables to remove every bit of broth. Discard the contents in the strainer and set the broth aside.
Use your hands to gently pull apart the chicken from the bone. It is very important to get all of the bones out of the chicken, which is a little tricky considering all of the tiny bones in the chicken breast. Double check your work carefully and discard all of the bones. Set the shredded chicken aside.
Dice the remaining 1/2 onion, 2 stalks of celery, and 1 large carrot.
Heat the olive oil in the same stock pot set over medium-high heat. Add the diced carrots, onion, celery, salt, and pepper and cook until tender, about 8 minutes.
Pour the broth back into the pot. Add the desired amount of the shredded chicken. Depending on the size of your chicken breasts, you may have too much. If this happens I usually reserve about a cup or so of the shredded chicken to toss onto salads for the week!
Bring a large pot of salted water to a boil. Cook the pasta until just shy of al dente, according to package instructions.
Meanwhile, stir the spinach into the soup until it is wilted. Season to taste with salt and pepper, if needed.
Place the desired amount of cooked pasta in the bottom of a soup bowl. Ladle the soup over the noodles. Serve and enjoy!