Pat the chicken wings dry with paper towels before seasoning. This helps the skin crisp properly during cooking. Combine all the rub ingredients in a small bowl and coat the wings evenly on all sides. Let the wings sit at room temperature for about 30 minutes before grilling.

While the wings rest, prepare the sauce. Add the ketchup, Louisiana hot sauce, brown sugar, cider vinegar, Tabasco, and Cajun seasoning to a saucepan over medium heat. Simmer for several minutes until slightly thickened.

Remove the sauce from the heat and whisk in the butter until smooth and glossy. Set the sauce aside while preparing the grill.

Preheat the grill for both direct and indirect heat cooking zones. Place the wings over direct heat and cook with the lid closed for about 5 minutes, turning once during cooking.

Move the wings to indirect heat and continue cooking for another 10 minutes. This slower cooking stage helps render the fat while keeping the meat tender and juicy.

Brush the wings generously with the prepared sauce and continue grilling. Turn the wings occasionally so the sauce caramelizes evenly without burning.

Continue cooking until the skin becomes dark golden brown with crispy edges and the internal temperature reaches at least 175°F. Add another light coating of sauce during the final minutes of cooking.

Remove the wings from the grill and let them rest for a few minutes before serving. Serve hot with ranch dressing, blue cheese, or your favorite dipping sauce.