Sauté Aromatics: Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery; cook 5–7 minutes until softened. Stir in garlic.
Simmer Broth: Add chicken, bay leaves, thyme, peppercorns, and Parmesan rind (if using). Pour in water/stock. Bring to a boil, then reduce to a gentle simmer. Skim off foam.
Cook Chicken: Simmer uncovered for 1 hour (or until chicken is tender). Remove chicken, shred meat, and return bones to pot for extra flavor (optional).
Strain & Finish: Discard bones, bay leaves, and Parmesan rind. Return shredded chicken to broth. Add pasta; cook until al dente (10–12 minutes).
Season & Serve: Stir in parsley, lemon juice, salt, and pepper. Ladle into bowls; top with grated Parmesan.