Saute 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-and-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.

Optional - Puree in a blender and return to heat.

Add cheese. Stir in nutmeg.