Start by preparing the chicken drumsticks. Pat them dry with paper towels to ensure the seasoning sticks well.
Butterfly the chicken drumsticks by making a slit along the length of each drumstick, being careful not to cut all the way through. Open them up slightly to allow for even cooking.
Brush the drumsticks with olive oil to act as a binder.
Generously season the drumsticks on all sides with the Cajun Rub.
Preheat your grill to medium-high heat.
Place the seasoned drumsticks on the grill and cook for about 15-20 minutes per side, or until the internal temperature reaches 165°F (75°C). Turn them occasionally to ensure even cooking.
Remove the drumsticks from the grill and let them rest for a few minutes to allow the juices to redistribute.
While the drumsticks are resting, prepare the Alabama White Sauce by combining mayonnaise, apple cider vinegar, Dijon mustard, brown sugar, prepared horseradish, hot sauce, cayenne powder, and honey in a medium-sized bowl. Mix thoroughly until smooth.
To serve, place the grilled drumsticks on a serving platter and drizzle generously with the Alabama White Sauce.
Enjoy your Cajun Grilled Chicken Drumsticks with Alabama White Sauce!