Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the chicken pieces and cook until browned on all sides, about 5 to 7 minutes. Remove the chicken and set it aside.
Add the chopped onion, carrots, and celery to the pot. Cook until the vegetables soften, about 5 minutes.
Stir in the minced garlic, thyme, and rosemary. Cook for 1 minute until fragrant.
Pour in the chicken broth. Bring the mixture to a simmer.
Return the cooked chicken to the pot. Add the gnocchi and cook according to package directions, usually about 3 to 5 minutes, until the gnocchi float.
Reduce the heat to low. Stir in the heavy cream and Parmesan cheese until the cheese melts and the soup thickens slightly. Do not boil after adding the cream.
Season the soup with salt and pepper to your taste.
Ladle the soup into bowls and garnish with fresh parsley before serving.
Notes
For a thicker soup, you can mix 1 tablespoon of cornstarch with 2 tablespoons of cold water and stir this slurry into the simmering soup before adding the cream.
You can substitute rotisserie chicken for the raw chicken breasts to save preparation time.
Use store-bought frozen gnocchi if preferred; adjust cooking time as needed.