Heat oil in a large Dutch oven or heavy pot over medium heat. Add onion, celery, and a pinch of salt. Cook 5 minutes until softened, then stir in garlic and cook 1 minute.

Push vegetables aside and add chicken in a single layer. Season with salt and pepper. Brown undisturbed 3 minutes, then stir and cook 2 minutes more until no longer pink on the outside.

Stir in buffalo sauce, diced tomatoes with juices, beans, and broth. Scrape up any browned bits from the bottom of the pot.

Bring to a boil, then reduce heat to low. Cover and simmer 20 minutes, stirring once, until chicken is tender.

Turn off heat. Add cream cheese chunks, let sit 1 minute, then stir until melted and creamy. Ladle into bowls and top with blue cheese crumbles, green onions, and extra buffalo sauce.