Cut chicken into bite-sized pieces. Spray slow cooker with cooking spray, and add chicken. Combine soup, sour cream, cheese, milk, Italian seasoning, and pepper in a medium-sized bowl. Pour over chicken in slow cooker.
Cube potatoes and add to slow cooker with chicken. Cover and cook on low for 6-7 hours.
Once potatoes are tender, add chopped broccoli and cook for an additional 30 minutes. Stir in sliced basil just before serving.