Melt the butter in a large stock pot over medium heat. Add the onion, carrots, and celery. Cook, stirring occasionally, until the onions are translucent, about 3 minutes. Season with the salt.
Add the buffalo sauce and cook until the liquid is reduced and thickened, about 8 minutes.
Add the chicken stock and bring the soup to a boil. Reduce the heat to medium-low and simmer until thickened, about 30 minutes. Remove the pot from the heat and stir in the heavy cream and shredded chicken.
Ladle the soup into the bread bowls and garnish with the crumbled blue cheese and scallions. Serve warm.