Shuck the corn, removing silk. Cut off stem to make a flat end. Stand corn on end and use a sharp knife to cut kernels from cobs. Measure 4 cups kernels; set aside. Stir together broth, milk and Angostura bitters; set aside.

In a 6-quart pot, melt butter over medium-low heat. Allow butter to bubble gently, stirring occasionally, until butter is light to medium brown. Add onions; stir and cook 3-4 minutes or until onions just start to brown. Stir in ham and continue to cook about 2 minutes more. Sprinkle in flour and gradually add milk mixture, stirring and scraping bottom of pot. Bring to a gentle boil over medium heat, stirring occasionally. Stir in corn, and black pepper to taste. Partially cover pot and simmer 15 minutes. Remove chowder from heat; stir in cheese and basil.