In a pan, heat the olive oil. Once adequately heated, add the celery, carrot, onion, garlic, salt, pepper, dried parsley, dried basil, and dried rosemary. Sauté the mixture for approximately 2 minutes or until the vegetables attain a slight translucence. While this step is optional, it is highly recommended for enhanced flavor.
In the crockpot, layer the raw chicken breasts, the sautéed vegetable mixture, and the diced potatoes. Proceed to add the chicken or bone broth. Cover the crockpot and set it to low for a duration of 6 hours.
Post-cooking, extract the quartered potato pieces and the chicken breasts from the crockpot.
In a blender, combine the extracted potato quarters, the preferred milk, and approximately 1/2 cup of the broth from the crockpot. Blend this mixture until it achieves a smooth consistency. Once blended, reintegrate this mixture back into the crockpot.
On a cutting board, shred the cooked chicken breasts. Subsequently, add the shredded chicken back into the crockpot.
Stir the soup in the crockpot until all ingredients are uniformly combined. For final presentation, garnish with fresh parsley before serving.