Steam potatoes until very tender; peel and cut into bite-sized pieces when cool.
Saute carrot, onion, and celery in the margarine until crisp tender. Stir in flour and bacon grease. Pour in chicken broth and milk and stir until smooth. Add potatoes and stir until mixture is lump-free.
Heat until ready to boil, but not boiling. Serve with grated cheddar cheese and chopped green onions.