In a large pot over medium heat, combine water, bouillon, potatoes and garlic. Bring to a boil, then stir in onion, celery and carrots. Reduce heat and simmer 15 minutes.
Stir in corn, peas and green beans and continue to cook on low heat.
Meanwhile, in a medium saucepan over medium heat, melt butter. Whisk in flour all at once to form a roux and let cook 10 seconds. Whisk in milk, a little at a time, and cook, stirring, until mixture is thick and bubbly. Stir in cheese until melted. Pour this mixture into the large soup pot, stir well and heat through.
