Saute onion and garlic in butter over medium heat. Remove onion. Add flour, stirring constantly. Add half and half, milk, and chicken stock. Bring almost to a boil. Add onion, brocoli and carrots and simmer on low heat for twenty minutes. Season the soup with salt, pepper, nutmeg, and cardamon. Stir in the cheeses and let simmer for ten minutes longer before serving.
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