Preheat oven to 450º. Remove liver, giblets, heart, and neck from inside turkey; discard or save to make stock.

Pat dry turkey. From the front of the breast, slide hands under turkey skin and loosen all the way to the back of the turkey. Place 10 sage leaves (5 on each side) under breast skin in a decorative pattern.

Salt and pepper turkey cavities (body and neck). Stuff with remaining sage leaves, apples, and onions. Skewer cavities shut. Rub outside of turkey with soft butter. Fold and tuck wings under turkey.

In a small saucepan, mix olive oil and broth. Saturate cheesecloth with liquid, squeezing out extra. Blanket turkey with cheesecloth. Use remaining broth for basting.

Place turkey on a rack in a large, heavy roasting pan. Place pan on lowest oven rack and immediately reduce temperature to 325°F. Bake for about 3 hours (17 minutes per pound), basting with oil-stock mixture every 20–30 minutes. (During last hour of cooking, cover lightly with foil, if necessary, to prevent overbrowning.) Remove cheesecloth during last 30 minutes of cooking. Insert meat thermometer in breast and thigh meat to judge doneness. Final breast temperature should be 170º, thigh 180°F.

Remove turkey from oven and let juices run into roasting pan. Tightly cover whole turkey with foil until ready to carve. Reserve pan juices to drizzle over slices before serving.