Ham and Cheddar Chowder

Melt butter in a 6-quart Dutch oven or soup pot over medium heat. Add onions, celery and carrot. Cook until very soft and translucent, but not brown. Add ham and cook until ham loses its water and is beginning to brown slightly. Add potatoes and stir to coat. Add chicken broth and pepper, simmer for about 25 minutes or until potatoes are tender. Bring to a rolling boil, mix flour and ½ cup of half-and-half with flour until smooth and add to the pot; stir until thickened and reduce heat to medium low. Add additional half-and-half to desired thickness. Add cheese and stir until melted. Add parsley. Cook for 10 minutes to meld flavors, stirring often to keep chowder from sticking.