Pour the broth into a large soup pot. Add carrots and celery and bring to a boil. Turn down and simmer till veggies are tender.
In another pan, melt the butter and cook onion over medium heat.
Whisk in flour and cook for a minute or two. Add milk, cooking till smooth and thickened.
Add milk mixture to broth.
Stir in cheese and cook till melted.
Season with salt and pepper.