Heat the olive oil in a large pot over medium heat. Place the chicken breasts in the pot and cook them for about 6-8 minutes per side, or until they’re fully cooked. Remove the chicken from the pot and set it aside.
Throw in the diced potatoes, sliced carrots, and celery. Stir them well, allowing the veggies to soften slightly for about 5 minutes.
Pour in the chicken broth and heavy cream. Sprinkle in the thyme, rosemary, salt, and black pepper. Stir everything together, bringing the mixture to a gentle boil. Reduce the heat to low and add the cooked chicken back into the pot. Cover and simmer for 20-25 minutes, allowing the flavors to meld and the potatoes to become tender.
Remove the chicken breasts from the soup. Use two forks to shred them into bite-sized pieces and then return them to the pot.
Taste the soup and adjust the seasonings if needed. Sprinkle fresh parsley on top for a burst of flavor and color before serving. And there you have it! Ladle out a bowl and enjoy.