In a small saucepan, combine celery, carrot and water. Bring to a boil, then reduce heat and simmer until tender. Meanwhile, in a large saucepan over medium heat, melt butter. Cook onion in butter until tender. Stir in flour and milk and cook until thickened. Stir in broth, cheese and vegetables with their liquid. Stir until cheese is melted and elements are well combined. Serve hot.