Cut the wings at each joint. Discard the wing tip or save it for stock.

Pour the vegetable oil into a large, heavy-bottomed pot until it reaches a depth of 4 inches, or use a deep fryer. Preheat the oil to 350°F.

Deep-fry the wings in batches for 8 to 10 minutes, stirring once to ensure even cooking. Depending on the size of your pot, you should be able to fry about 5 or 6 wings at a time. When the wings are just beginning to brown, remove them from the oil and drain them on a wire rack resting on a cookie sheet.

Combine the melted butter and Cajun seasoning in a large bowl. Place the fried wings in the bowl and toss to coat.