In a small bowl, mix together the kosher salt, ground black pepper, and light brown sugar to create a dry brine. To spatchcock the turkey, place the turkey breast side down on a cutting board. Using sharp kitchen shears, cut along both sides of the backbone and remove it. Using a chef’s knife, make a small incision down the length of the breastbone, then flip the turkey skin side up and press firmly to flatten the bird, you should hear a crack. Place the prepared turkey on a wire rack set inside a large rimmed baking sheet, skin side up. Rub the dry brine all over the turkey, ensuring it is well-coated. Chill the turkey, uncovered, in the refrigerator for 12–18 hours; the skin should become tight and dry.
Place an oven rack in the bottom third of the oven and preheat it to 425°F (220°C). Remove the wire rack with the turkey from the baking sheet and set aside. Rinse off any excess salt from the baking sheet and dry it thoroughly. Line the baking sheet with a few layers of aluminum foil to make cleanup easier, then return the rack with the brined turkey (from Step 1) to the prepared baking sheet. Tuck the wing tips behind the breast to protect them from burning. Let the turkey sit at room temperature for 30 minutes before roasting. I like giving the bird this time to come closer to room temp as it helps ensure even roasting.
In a small bowl, combine the unsalted butter (at room temperature), fresh thyme leaves, and finely minced garlic cloves to make a fragrant flavored butter. Gently separate the turkey skin from the meat as much as possible without tearing it, and using your hands, carefully rub the butter mixture under the skin to flavor the meat directly. Then, rub the entire turkey all over with extra-virgin olive oil to help the skin crisp and brown during roasting.
Pour 1/2 cup water into the foil-lined baking sheet to prevent drippings from burning and add some extra moisture as the turkey cooks. Place the prepared turkey (from Step 3) breast side up on the rack and roast in the preheated oven. Rotate the baking sheet halfway through cooking for even browning. Roast until the skin is deep golden brown and crisp, and an instant-read thermometer inserted into the thickest part of the breast registers 150°F, about 1 hour and 25 minutes. (Start checking after 1 hour; or use a meat thermometer probe that can stay in during roasting.)
When the turkey is fully roasted, transfer it to a cutting board. Let it rest for 15–20 minutes to allow the juices to redistribute before carving. I always let the turkey rest—this keeps it moist and juicy when you slice into it.