Butterfly each drumstick by slicing down one side along the bone with a sharp knife, then gently opening the meat without cutting through.
Pat the drumsticks dry, coat lightly with avocado oil, and season generously on every side with Cajun seasoning, including the opened cut.
Preheat your pellet grill or smoker to 275°F. Smoke the drumsticks over indirect heat for 25 to 30 minutes.
While the chicken smokes, warm the butter, honey, garlic, Cajun seasoning, and red pepper flakes in a small saucepan over low heat until smooth.
Move the drumsticks over direct heat and rotate frequently until the skin chars and crisps.
Brush thin layers of Cajun honey butter over the chicken during the last several minutes, flipping between coats so the glaze builds without burning.
Cook until the internal temperature reaches 175°F to 185°F in the thickest part of the meat, away from the bone.
Brush with one final coat of Cajun honey butter, rest 5 minutes, then top with fresh chopped parsley and serve.
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Notes
Grill Master Tip: Butterfly every drumstick and apply the glaze in several thin coats instead of one heavy layer. You'll build a richer glaze while keeping the honey from burning. Store leftovers in an airtight container up to 4 days and reheat at 350°F in the oven or air fryer.