Melt the butter and saute the onions in the butter until soft. Sprinkle the flour over the onions and butter. Cook and stir over medium heat for 1-2 minutes.
Whisk in the heavy cream and chicken stock. Add the broccoli and carrots. Cook over low heat for 20-25 minutes or until the broccoli and carrots are tender.
Add Kosher salt and pepper to taste. At this point you can leave the soup chunky, or what I like to do is blend about 1 cup of the soup and stir it in for a smoother soup. Return to low heat and add the cheese. If your heat is too high your soup can get grainy. Stir in the nutmeg and check seasoning one last time before serving.
Serve with crusty sourdough bread or in a nice crusty sourdough boule. Enjoy!