Cajun Barbecued Turkey

Rinse turkey inside and out. Pat dry with paper towels. Sprinkle turkey cavities with 2 tablespoons Cajun spice mix.

Whisk broth and butter in small bowl to blend. Season to taste with salt and pepper. Using kitchen syringe, inject mixture into turkey breasts, thighs, and drumsticks. Rub oil over turkey. Sprinkle turkey with remaining 2 tablespoons Cajun spice mix.

IF USING CHARCOAL BARBECUE:
Mound lump charcoal in barbecue and burn until light gray. Using tongs, carefully divide hot charcoal into 2 piles, 1 pile at each side of barbecue. Sprinkle each pile with generous 1/2 cup mesquite chips. Place empty broiler pan between piles. Position grill at least 6 inches above charcoal. Position vents on barbecue so that chips smoke and charcoal burn but do not flame.

IF USING GAS OR ELECTRIC BARBECUE:
Preheat barbecue with all burners on high. Turn off center burner and lower outside burners to medium-low heat. Place generous 1/2 cup mesquite chips in each of 2 broiler pans. Set pans over 2 lit burners. Place empty broiler pan over unlit burner. Position grill at least 6 inches above burners.

Tuck wing tips under turkey body. Tie legs together to hold shape. Sprinkle turkey with salt and pepper. Arrange turkey breast side up on grill, centering above empty broiler pan. Cover and cook until thermometer inserted into thickest part of thigh registers 165 degrees F, adding 1 cup mesquite chips (and 7 charcoal pieces if using charcoal barbecue) to barbecue every 30 minutes, about 3 hours.

IF USING SMOKER:
Set up your smoker for smoking, following the manufacturer's instructions. Preheat smoker to 225 degrees F. Wash, rub, and inject turkey as described above. Place turkey in smoker. If using a water smoker, place 1 quart water, wine or cider in water pan. For extra flavor, add 1/4 cup Cajun spice mix to water. Smoke turkey until instant-read meat thermometer registers 165 degrees F when inserted into thickest part of turkey thigh, about 6 hours.

Transfer the turkey to a platter, tent with foil to keep warm, and let rest for 10 minutes. Carve and serve.