Place a large stockpot over medium heat. Add the butter, onions, and garlic. Saute for 3-4 minutes to soften. Then add the flour and stir well so that the flour coats the onion pieces.
Pour in the broth and low-fat milk. Then stir in the broccoli florets, sea salt, cayenne pepper, and nutmeg. Bring to a boil, then reduce the heat and simmer for about 15 minutes, until the largest broccoli florets are tender.
Finally stir in the shredded cheese. Stir to thicken the soup as the cheese melts. Then turn off the heat and serve.