Heat the oil in a deep-fat fryer according to the manufacturer's instructions. Or, if you're using a skillet pour in about an inch of oil and heat over medium-high heat to 370 degrees.
Cut up chicken wings into three parts, discard wing tip. Add the chicken wings and cook them until golden brown and crisp on both sides, about 8 minutes in all. Using a slotted spoon, transfer the wings to paper towels to drain off any excess oil.
Combine all of the ingredients for the sauce in a large saucepan and stir over medium-high heat until the sauce begins to simmer.
Reduce the heat to low and add the chicken wings. Simmer the dish until it's hot throughout, about 10 minutes.
To make the Bleu Cheese Dipping Sauce: Stir the mayonnaise and the bleu cheese together. Use right away or chill until serving time.