1Saute carrot, celery, and onion in butter in a small Dutch oven until tender.
2Add the flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until the mixture is thickened and bubbly. Add salt and pepper; stir well.
3Add the cheese and ham; stirring until the cheese melts. Serve immediately.