In a 4-quart slow cooker combine potatoes and onion. Pour broth over vegetables.
Cover and cook on high-heat setting for 3 hours.
In a medium bowl combine cornstarch, dried thyme, and pepper. Whisk in evaporated milk. Slowly stir the cornstarch mixture, ham, and carrots into the hot soup. Cover and cook for 30 minutes more, stirring the soup occasionally.
Serve soup topped with broccoli, cheese, and fresh thyme.