Saute onion in butter. Set aside. Whisk butter and flour over medium heat for 3-5 minutes. Stir constantly and slowly add half and half. Add chicken stock, still whisking.
Simmer 20 minutes. Do not cover! (Only say this because I might have covered it, tried to start some laundry…..until I heard frying sounds and saw smoke coming from the kitchen!)
Add broccoli, carrots and onion. Cook over low heat until veggies are tender – about 20-25 minutes. Add salt and pepper. The soup will have thickened by now.
Carefully transfer soup mixture to blender and puree. Return soup to pot (or crockpot) over low heat. Add cheese. Stir until well blended. Add nutmeg right before serving.
Makes 8-10 servings.