Blue Cheese Dressing:

1 cup crumbled blue cheese

1/2 cup buttermilk

1/2 cup mayonnaise

2 to 4 tablespoons whipping cream, half-and-half, or milk

2 teaspoons Worcestershire sauce

1/2 teaspoon salt

1/4 teaspoon freshly ground black pepper

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24 chicken wings

1 teaspoon salt

1 teaspoon freshly ground black pepper

1 to 3 tablespoons hot sauce

4 tablespoons unsalted butter

1 tablespoon vinegar, any kind

4 cups flavorless cooking oil

Carrot sticks and/or celery sticks, for serving

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To make the dressing, in an electric blender, place 1/2 cup of the blue cheese and all the remaining ingredients and liquefy. For a thinner consistency, all a little more whipping cream. Stir in the remaining 1/2 cup blue cheese. This can be done up to 12 hours before cooking, and then stored, tightly covered, in the refrigerator.

Cut off and discard the chicken wing tips. Cut the wings in half through the joint. You will have 48 pieces. Rub the chicken with salt and pepper. Place the hot sauce, butter, and vinegar in a small saucepan. Bring the mixture to a simmer, then set aside.

Place a 12-inch frying pan over medium-high heat on an indoor stovetop or an outdoor gas grill. Add the cooking oil. Heat the oil until bubbles form around the end of a wooden spoon dipped into the oil, 350 to 375 degrees F. Turn the heat to high. Add half the wings. Deep-fry until the wings become deep golden and the meat is cooked along the bone (cut into one with a paring knife), about 12 minutes. Transfer the wings to a wire rack to drain. Cook the second batch of wings. place the wings on a serving platter. Pour the butter sauce over the wings. Serve with the dressing and the carrot sticks.