PARMESAN BROTH: In a large soup pot, melt a tablespoon of butter over medium heat. Add half the onions, chunks of carrots, and celery, and saute for 4 minutes. Add mushrooms, bay leaf, thyme, and cheese rinds. Let cook for another 4 minutes. When the cheese and vegetables start sticking to the bottom of the pot, start slowly pouring in the hot water as you stir and scrape to help deglaze the pan. When deglazed, add the remaining water and kosher salt. Bring to a simmer, stir and make sure nothing is stuck.
SIMMER: Lower the heat to medium-low and let simmer for 50-60 minutes, stirring often to ensure the cheese isn’t sticking to the bottom. You should see steam billowing off the pot but no visible bubbling in the stock. Strain the broth, and set aside for now.
SOUP: To the same soup pot, add the remaining tablespoon of butter and a tablespoon of oil. Sauté the remaining onions, carrots, and celery with a pinch of salt for 7 minutes. Add the garlic and saute for 1 minute. Add 8 cups of prepared stock and bring to a simmer. Add the shredded chicken and pasta and cook for 6-7 minutes or as indicated on the package, stirring often to keep the pasta from sticking.
FINISH: When the pasta is done, turn off the stove, add the lemon zest and juice. Taste and adjust with salt as desired, you shouldn’t need too much more. Serve warm topped with parm and parsley on top.