Place the water, carrots, celery, and green onions in a medium pot over high heat. Bring to a boil for 5 minutes over high heat. Set aside, but do not drain.
Melt the butter in a large stockpot over medium heat. Add the onion and sauté for 1 minute. Then add the flour and stir.
In a large saucepan, bring the milk and broth to boil.
Whisk the broth mixture into the flour mixture. Then add the rest of the ingredients, as well as the boiled vegetables and the water in which they were cooked. Bring to a boil and serve immediately.
