In a large soup pot, melt 1 tablespoon of butter over medium heat. Add half of the diced onions, along with chunks of carrots and celery, and sauté for 4 minutes until the vegetables are slightly softened. Stir in the rehydrated mushrooms, bay leaf, thyme, and parmesan rinds; continue cooking for another 4 minutes. Gradually pour in 8 cups of hot water and sprinkle with kosher salt, then bring to a gentle simmer. Let the broth simmer for 50-60 minutes while you prepare the soup.

Once the broth has simmered, strain it through a fine-mesh sieve and return the pot to the heat. Add the remaining tablespoon of butter and a splash of olive oil. Sauté the remaining diced onions, carrots, and celery over medium heat for 7 minutes, stirring often until they begin to soften. Stir in the minced garlic and sauté for an additional minute.

Pour in the prepared parmesan broth into the pot with the sautéed vegetables. Bring the mixture to a simmer over medium heat.

Stir in the shredded cooked chicken and add the stelline pasta to the simmering broth. Cook for 6-7 minutes, or until the pasta is al dente.

Ladle the warm Parmesan Chicken Pastina Soup into individual bowls, top with freshly grated parmesan and chopped parsley.