Heat butter in a large pot over medium-high heat. Add diced celery and onion, cooking until tender.
Sprinkle flour over the veggies, stirring until absorbed.
Gradually pour in chicken broth, stirring constantly to avoid lumps.
Add shredded chicken, Buffalo wing sauce, salt, pepper, and ranch seasoning. Stir well.
Let the soup simmer for 10-15 minutes.
Stir in heavy cream or half-and-half.
Serve hot, garnished with sliced green onions.