Four days before cooking, make the rub mixture and season the turkey: Coarsely grind the peppercorns and allspice berries by pulsing 3 to 4 times in a blade-style coffee/spice grinder. Add the dried thyme and pulse 3 more times. Combine the salt, rubbed sage, and ground spices in a small bowl and set aside.
Position the turkey, breast-side down with the tail facing you, on a silicone mat or other stable surface set inside a large sheet pan. Use heavy-duty kitchen shears to cut up one side of the backbone. Turn the bird and cut back down the other side of the spine. Reserve the backbone for stock or gravy. Discard any fat pockets or excess skin found inside the bird. Flip breast-side up and use the heel of your hands to press down on both breasts, until you hear a cracking sound and the bird flattens.
Place the turkey, breast-side up, on a rackI use a standard cooling or cake rack. set inside a sheet pan, and turn the wings backwards, tucking the tips under the forewings. Flip the turkey breast-side down and season with half of the rub mixture. Then, flip the bird back breast-side up and season with the remaining mixture.
Store, uncovered, on the lowest level of your refrigerator for 4 days.
When ready to cook, allow the turkey to sit at room temperature for 1 hour. Place one oven rack in the center of the oven and a second one just below it. Place an empty roasting pan or large rimmed sheet pan on the lower rack. Crank the oven to 425°F.
Place the turkey, still on the cooling rack, directly on the center oven rack. Add a cup of water to the pan below to prevent any drippings from smoking. Roast for 30 minutes.
Reduce the heat to 350°F and continue to roast the bird until a probe thermometer inserted into the thickest part of the breast registers 155°F, an additional 40 to 50 minutes.
Remove the turkey and its rack and rest for 15 minutes before carving. Carryover heat will take the final temperature close to 165 degrees.