In a medium pot, melt the butter over medium heat.
Once melted, add the onions and carrots and sauté for 3-5 minutes.
Add the rice flour to the pot, mix well and cook for a minute or so.
Add the half-and-half, chicken broth, broccoli, and a couple pinches of black pepper and mix well.
Reduce heat to medium low and cook for 15-20 minutes, stirring occasionally, until the vegetables are tender.
When the vegetables are tender, add the nutmeg, if using, and turn the heat off.
Add the cheese a little at a time, stirring in each addition until it is mostly melted into the soup before adding more.
If needed, turn the heat back on to medium-low and warm the soup through, but do not boil.
Serve soup with your favorite gluten free rolls or crackers.