- In a bowl, using the back of a fork, mash the blue cheese into pea-size pieces. Add the mayonnaise and buttermilk and whisk until well combined. Season with salt and pepper. Transfer the dip to a small bowl, cover with plastic wrap and refrigerate until ready to serve. (The dip can be made up to 2 days in advance.)
- Pour the oil into a large pot, making sure the oil does not come more than halfway up the sides. Heat the oil to 375°F on a deep-frying thermometer.
- Preheat an oven to 200°F. Line a baking sheet with paper towels.
- Cut through the joint on each chicken wing to separate the wing into 2 pieces. Season with salt and pepper. Put the flour in a bowl. Dredge the wings in the flour, shaking off the excess.
- Working in batches, fry the wings until golden brown and crispy, 8 to 10 minutes. Transfer the wings to the paper towel-lined baking sheet and keep warm in the oven.
- In a small saucepan over medium heat, combine the hot wing sauce and butter and heat until the butter melts. Alternatively, in a small microwavable bowl, whisk together the hot wing sauce and butter and warm in a microwave at 15-second intervals until hot.
- Transfer the fried chicken wings to a large bowl. Pour the sauce over the wings and stir to coat evenly. Serve immediately with the blue cheese dip and celery stalks. Serves 4 to 6.