Heat the butter in a large stock pot over medium-low heat. Add in the onion, carrots, celery, and garlic with a big pinch of salt and pepper. Cook, stirring occasionally, until the vegetables soften.
Stir in the minced garlic and poultry seasoning. Stir in the shredded chicken.
Add in 7 cups of chicken stock and the parmesan cheese rind. Bring the mixture to a boil, then reduce it to a simmer. Stir in the stelline pasta. Cook uncovered, stirring occasionally, until the pasta is al dente, about 8 minutes.
Add in the lemon juice and fresh parsley. Taste the soup and adjust seasoning as needed. If the parmesan rind didn’t melt entirely, you can scoop it out.
Serve immediately with a lemon wedge for sprinkling, parmesan cheese for topping, and more parsley sprinkled on top.
For leftovers, consider cooking the pasta separately.