Heat butter in a 3-quart heavy bottom pot. Add onions and garlic and saute about 5 minutes. Then add you chicken broth and stir.
Next add broccoli, cream, milk, salt, pepper, and nutmeg. Bring up to a boil and then simmer for about five minutes until the broccoli is tender.
Finally, stir in your cheese until it melts.
Serve warm garnished with some extra cheese.
I recommend aged cheddar cheese that you grate yourself. Just give it a quick spin in the food processor. Zip, zip and it's done. The pre-grated type that comes in a zip lock bag contains preservatives meant to keep the shreds from clumping together in the bag. It doesn't melt quite as well.
I love the delicate flavor of this soup. There are a few add-ins you could go with. Cinnamon would be very nice with this soup. If you like some spiciness, a pinch of cayenne pepper will do the trick. Or you could add chopped bacon, bite-size cooked chicken or turkey, or cooked, diced potatoes (if you're not low carb). It's up to you.