Melt butter in large Dutch oven or large pot. Add onion, celery & cook until onions soften.
Add stock & potatoes. Simmer, covered for 10-15 mins, or until potatoes are tender.
Blend flour & milk - mix well. Pour this mixture into the soup & stir until soup boils & thickens.
Stir in cheese and half the green onions. Season to taste with salt and pepper.