Combine the broccoli, carrots, and onion in a slow cooker.
Add the chicken stock, salt, pepper, and nutmeg. Set your slower cooker to LOW for 4 and a half hours. (All slow cookers are different if your broccoli is not very tender after four hours, add more time.)
At four hours turn the slow cooker to HIGH so that you can complete the process with the temperature raised.
Add the cheese a little at a time. Start by adding a half cup, covering and letting it melt and then stirring it, before then adding another half cup.
Finally, stir in the half and half. Serve immediately.