saute onions and garlic in the butter over medium heat. add flour stirring constantly. add half and half, chicken stock, and milk bring to almost boil. put in the broccoli and carrots and simmer for 20 minutes.

season soup with the nutmeg, cardamom, and salt/pepper. stir in the cheeses and let simmer for 10 minutes longer before serving.

as a side note you can mess around with different cheeses and different amounts to your liking.