Slowly begin to add the half and half, stirring constantly to combine to help prevent lumps.  Add the milk in the same way, followed by the chicken or veggie stock (for vegetarian version), whisking constantly.  Once completely combines and is smooth, turn down heat to a simmer and allow soup to cook for 20 minutes.

Add all the broccoli, reserving 1/2 cup and carrots to the pot and continue to cook over low heat until veggies are tender and soup is thickening, about 20 minutes.

Chop remaining broccoli into small pieces and steam using the microwave until crisp tender.  Set aside until end.

Pour batches into a blender or food processor and purée.  Return the soup back to the pot over low heat and add the cheese.  Add the nutmeg and stir until well blended.  Season to taste with salt and pepper, stir in reserved broccoli pieces and serve immediately.  Garnish with a little shredded cheese if you desire.

Makes 4 servings.