Sauté the onion and garlic in the butter over medium heat. Add in the flour, stirring constantly. Add in the half and half, milk, and chicken stock. Bring to almost a boil.
Add the broccoli and carrots. Simmer on low heat for about 20 minutes.
Season the soup with Beazell's Cajun Seasoning and add the nutmeg. Stir in the cheeses (and you can play around with the amounts; use however much or as little you like) and let simmer for 10 minutes longer before serving.
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