Fill a small pot with water and set it on the stove over high heat. Bring it to a boil while you prepare the rest of the soup.
In a Dutch oven or large soup pot, add either butter or olive oil over medium heat. Toss in your diced onion, carrots, and celery. Sauté for about 5-7 minutes until softened.
Add minced garlic along with kosher salt and pepper. Cook for another minute until fragrant.
Add diced or shredded cooked chicken to the pot. Pour in the chicken broth and stir to combine. Add bay leaves.
Bring to a boil over medium-high heat, then reduce to a simmer. Cook for about 15-30 minutes.
Cook gluten-free pasta according to package directions, undercooking by 1-2 minutes.
Once pasta is ready, drain and gently fold into the soup along with parsley and optional dill. Remove bay leaves before serving.