Add olive oil to a large Dutch oven set over medium heat. Once shimmering, add onion, celery, and green pepper. Sauté until fragrant and softened, about 5 minutes. Add the garlic and continue to sauté an additional minute.
Sprinkle with flour and stir to combine. Slowly pour the broth followed by the chicken, beans, spices, and buffalo sauce. Store to combine and cover, cooking for about 20 minutes over low heat.
Slowly add the half and half, stirring to combine. Allow to continue to slowly simmer as you prepare the blue cheese crostini.
To make the blue cheese crostini, broil slices of baguette or ciabatta lightly in your oven. Once lightly toasted on both sides, top each slice with blue cheese and return to the oven. Broil for another 1 minute, or until cheese is softened.
Serve with bowls of chili topped with extra buffalo sauce, shredded cheese, chopped green and red onions, and cooked bacon.