The secret to moist turkey: Brining. A brief soak in a salty solution helps maintain moisture during cooking. I add beer and pepper flakes to the brine, especially when I’m pairing the turkey with a sweet and tangy adobo sauce.
Put 2 ½ quarts water, sugar, salt, and pepper flakes into a very large deep pot. Stir the mixture to dissolve the sugar and salt. Add the beer; mix well.
Split the turkey breast down the breast bone into two pieces. Put turkey in the beer brine, making sure it is submerged. Refrigerate covered 6 to 8 hours.
Soak mesquite chips in water to cover for at least 30 minutes. Heat a gas grill to medium-high or light a charcoal fire and let it burn just until the coals are covered with gray ash and very hot.
When the grill is ready, either turn the burner(s) in the center to medium-low or bank the coals to the sides for indirect cooking. Add some of the soaked wood chips to the grill (for a gas grill, place them in a smoker attachment box or wrap the chips in foil; for charcoal, place them on the hot coals). For the charcoal grill, set the grill grate in place.
Remove turkey from the brine and pat thoroughly dry with paper towel. Rub the turkey with garlic and sprinkle with herbs. Set the turkey breast halves on a roasting rack set inside a heavy-gauge foil pan. Drizzle lightly with oil.
Set the pan on the cooking grate. Pour 1 cup water into the turkey pan. Cover the grill and cook over medium heat. To maintain an even temperature with a charcoal grill, add more charcoal regularly (usually a few pieces every half hour or so). Keep adding wood chips as desired to give smokiness.