Slice the carrots, celery, and dice the onion. Mince the garlic. If using large chicken thighs or breasts, cut them into bite-sized pieces or leave them whole to shred later.
In a large pot, melt the butter over medium heat. Add the diced onion, sliced carrots, and celery. Sauté for 5-7 minutes until softened. Add the minced garlic and cook for another minute until fragrant.
Place the chicken thighs (or breasts) in the pot with the vegetables. Season with salt and pepper.
Add the chicken bone broth to the pot, ensuring the chicken is submerged. Drop in the parmesan rind for extra depth of flavor. Bring to a boil.
Once boiling, reduce the heat to low. Cover and let it simmer for 25-30 minutes until the chicken is cooked through and the flavors meld together.
Remove the chicken from the pot and shred with two forks or chop into bite-sized pieces. Return to the pot and stir.
Remove and discard the parmesan rind. Ladle into bowls and top with freshly grated parmesan cheese. Garnish with fresh parsley, diced jalapeño, or a squeeze of lemon if desired.