In a large soup pot, melt a tablespoon of butter over medium heat. Add half the onions, chunks of carrots, and celery, and saut? for 4 minutes. Add mushrooms, bay leaf, thyme, and cheese rinds. Let cook for another 4 minutes. Slowly drizzle in the hot water as you stir and scrape to deglaze the pan. Add the remaining water and kosher salt. Bring to a simmer, stirring to ensure nothing is stuck.

Lower the heat to medium-low and let simmer for 50-60 minutes, stirring often to prevent the cheese from sticking. Strain the broth and set aside.

In the same soup pot, add the remaining tablespoon of butter and a tablespoon of oil. Saut? the remaining onions, carrots, and celery with a pinch of salt for 7 minutes. Add the garlic and saut? 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. Turn off the stove, add the lemon zest and juice. Adjust with salt as needed. Serve warm topped with Parmesan and parsley.