Cook bacon in a large heavy sauce pan. Reserve about 2 Tablespoons bacon fat in pan. Add butter, chopped onion and celery. Cook, stirring, until vegetables are tender. Stir in the sliced green onion and flour until blended. Stir in chicken broth, cover and continue cooking, stirring frequently, until the mixture is thickened and vegetables are very tender. Stir in half and half, diced potatoes, salt, pepper, and cheese. Continue cooking until cheese is melted. Blend about half of the soup with an immersion blender her. Serve the soup garnished with bacon and extra sliced green onion.