In a large saucepan; over medium heat, cook carrot, celery and onion in butter until tender, about 5-7 minutes, stirring occasionally. Stir in flour. Cook stirring constantly, until smooth and thickened, about 2 minutes. Gradually stir in broth and milk. Cook and stir over medium heat until slightly thickened. Reduce heat to low. Stir in cheeses. Cook, stirring constantly, until cheeses have melted and soup is smooth. Stir in pepper. To serve, ladle into bowls. Top with chives and bread, if desired.