How to Make It
Place turkey, breast side down, on a work surface. Using poultry shears and beginning at tail end, cut along each side of backbone, separating backbone from turkey. Reserve for stock or discard. Turn turkey breast side up. Using the heels of your hands, press firmly against breast-bone until it cracks and turkey breast flattens. Trim any excess fat around neck.
Starting at neck end, loosen and lift skin from breast and legs by inserting fingers and gently pushing between skin and meat (do not detach skin completely). Rub 1 tablespoon salt under skin. Carefully replace skin. Rub remaining 2 1/2 tablespoons salt all over skin and in turkey cavity, rubbing more salt where meat is thickest. Place turkey on a wire rack set snugly inside an 18- x 13-inch rimmed baking sheet. Tuck wing tips under turkey. Turn turkey breast side down. Cover with plastic wrap; refrigerate 36 hours.
Spread limes and ginger in a single layer on a clean rimmed baking sheet (lined with aluminum foil, if desired); add garlic head halves. Place a wire rack on lime mixture in baking sheet. Remove turkey from refrigerator. Uncover turkey, and place, breast side up, on rack in prepared baking sheet; pat dry with paper towels. Refrigerate, uncovered, at least 6 hours or up to 12 hours.
Remove turkey from refrigerator. Let stand at room temperature 1 hour. Meanwhile, preheat oven to 450°F with oven rack in lower third of oven. Place 2 butter pieces under loosened skin of each breast and 2 butter pieces under loosened skin of each leg. Pour stock into baking sheet.
Roast turkey in preheated oven until an instant-read thermometer inserted in thickest part of breast registers 150°F, 1 hour to 1 hour and 10 minutes, rotating baking sheet halfway through roasting time. Transfer turkey to a cutting board, and let rest 30 minutes. (Reserve aromatics and pan drippings for Coconut-Lemongrass Gravy.) Carve turkey, and transfer to a platter. Serve with Coconut-Lemongrass Gravy.
For dry brining, select natural, heritage, or organic turkeys instead of kosher, water-added, or self-basting turkeys, which are processed with salt.