Heat olive oil in a large pot or Dutch oven over medium heat. Add chicken breasts and cook until browned on both sides. Remove chicken and set aside.
Add onion, carrots, and celery to the pot and cook until softened, about 5-7 minutes.
Add garlic, thyme, and rosemary and cook for 1 minute more.
Pour in chicken broth and bring to a simmer. Add the cooked chicken back to the pot and cook until chicken is cooked through, about 10-15 minutes. Remove chicken and shred with two forks.
Add gnocchi to the soup and cook according to package directions until gnocchi are tender.
Stir in heavy cream and Parmesan cheese. Season with salt and pepper to taste.
Add the shredded chicken back to the soup. Garnish with fresh parsley and serve.
Notes
Serve hot and enjoy! Leftovers can be stored in the refrigerator for up to 3 days.