Place the maple sugar, paprika, black pepper, coarse salt, celery salt, garlic and onion powders, cayenne, and mustard in a small bowl and stir to mix.
Rinse the turkey breast under cold running water, then drain and blot dry with paper towels. Using poultry shears or a large knife, cut out the ribs so the turkey breast lies flat.
Trim off and discard any excess fat. Sprinkle the rub over the turkey on all sides, patting it onto the meat with your fingertips. Place the breast in a covered bowl or resealable plastic bag and let cure overnight in the refrigerator.
Make the Basting Mixture:
Combine the maple syrup and melted butter in a small saucepan.
Set up the grill for indirect grilling and preheat to medium. If using a gas grill, place all of the wood chips or chunks in the smoker box or in a smoker pouch and run the grill on high until you see smoke, then reduce the heat to medium. If using a charcoal grill, place a large drip pan in the center, preheat the grill to medium, then toss all of the wood chips or chunks on the coals.
When ready to cook, place the turkey breast in the center of the hot grate, over the drip pan and away from the heat. Cover the grill and cook the turkey until cooked through, 1-1/4 to 1-1/2 hours. To test for doneness, use an instant-read meat thermometer: The internal temperature should be about 170 degrees F. After 45 minutes, brush the turkey breast with some of the maple butter basting mixture. Baste the turkey 2 or 3 more times with the maple butter. If using a charcoal grill, after 1 hour you'll need to add 12 fresh coals to each side.
Transfer the grilled turkey breast to a cutting board and let it rest for 5 to 10 minutes, then carve. Or refrigerate the turkey until completely chilled and serve it cold.
Notes
VARIATION: While I call for a turkey breast here, you could certainly smoke a whole turkey the same way. For a 10-pound turkey, you'd need a double batch of the rub and basting mixture. The cooking time would be 2-1/2 to 3 hours.