Place water, carrots, celery, onion and chicken stock in a large cooking pot. Bring to a boil over medium-high heat; cover, reduce heat and simmer for 10 to 12 minutes or until vegetables are tender. â€¨â€¨Place the flour in a 2-cup glass measure and slowly whisk half of the milk into flour. Stir flour/milk mixture into vegetable mixture, mixing well. Add remaining milk and cook until thickened, about 15 minutes.
Add cheese and stir until well blended. Season to taste with salt and pepper.