1In a large pot over medium heat, combine broth, broccoli, onion, carrots and bay leaf. Bring to a boil, then reduce heat and simmer until vegetables are tender. Remove bay leaf. (At this point, you may remove the broccoli stalks, carrots and onion and puree in a food processor, then return them to the pot, if desired.)
2Stir in the cheese until melted. Adjust seasonings. Stir in half-and-half and heat through.