Add 3-inches of oil to a heavy-bottomed 5-quart pot. Heat the oil over medium-high heat until it reaches 350° F. Carefully add half of the chicken wings (straight from the refrigerator) and fry until golden, about 10 minutes. Place the fried chicken wings on a paper towel-lined plate to drain the excess oil. Fry the remaining chicken wings the same way.
In a small skillet over medium heat, melt the butter. Then stir in the hot sauce. Remove from heat.
To a large bowl, addd the fried wings and hot sauce mixture. Gently toss to coat the wings. Serve with celery sticks and blue cheese dressing.
Notes
If you like your wings extra crispy, fry them up for up to 15 minutes instead of 10.