Sauté onion in butter. Set aside.
Cook melted butter and flour using a whisk over medium heat for 3-5 minutes. Stir constantly and add the half & half.
Add the chicken stock. Simmer for 20 minutes.
Add the broccoli, carrots and onions. Cook over low heat 20-25 minutes.
Add salt and pepper to taste. Can be puréed in a blender but I don’t. Return to heat and add cheese. Stir in nutmeg.