In saucepan, boil asparagus spears and onion in 2 1/2 cups water until tender.
Mash softened vegetables and pass through fine strainer or cheesecloth. Put strained vegetable puree back into stock. Add butter, milk, cube, salt and cornstarch. Cook over moderate flame until smooth and thick, stirring continuously with wire whisk. Add grated cheese and simmer for a few minutes. Serve hot.