Wash and chop the vegetables. Dice the onion, mince the garlic, and slice the carrots and celery.
Heat the olive oil in a large skillet over medium heat. Add the chicken breasts and cook for 5-7 minutes on each side until golden brown. Remove and set aside.
In the same skillet, add the diced onion and sauté for 5 minutes until translucent. Stir in the minced garlic and cook for an additional minute. Transfer to the slow cooker.
In the slow cooker, add the sliced carrots, celery, cooked chicken, chicken broth, frozen peas, corn, thyme, rosemary, salt, and pepper. Stir gently.
Cover the slow cooker and cook on low for 6-7 hours or on high for 3-4 hours.
Once the chicken is cooked, shred it and return to the soup. Stir in the heavy cream and let cook on low for an additional 15-20 minutes.