Preparation

Butter and salt the turkey

• Line a 12×16-inch heavy-duty roasting pan with 2 layers of paper towels. Blot the turkey dry inside and out.
• In a small bowl, combine the butter with 2 tsp. salt and 1 tsp. pepper; stir in the rosemary, thyme, garlic, lemon zest, and orange zest. Set aside 1/4 cup of the butter mixture for making the gravy.
• Slide your hand under the turkey’s skin to loosen it from the breast and thigh meat. Using your fingers, spread the butter directly on the breast and thigh meat, being careful not to tear the skin. Season the turkey inside and out with 1-1/2 tsp. each salt and pepper. Tuck the wings behind the neck and tie the legs together with kitchen twine.
• Set the turkey breast side up in the prepared pan. Loosely cover with waxed paper or parchment and refrigerate for 1 to 2 days.

Make the broth for the gravy

• Position a rack in the center of the oven and heat the oven to 400°F. On a large rimmed baking sheet, toss the turkey neck, tail, giblets (excluding the liver), onion, and celery with the oil; arrange in a single layer. Roast, stirring once, until well browned, about 40 minutes.
• Transfer the roasted ingredients to a heavy-duty 5-quart pot. Pour 1 cup of the chicken broth onto the hot baking sheet and scrape up any browned bits from the bottom with a wooden spatula; transfer to the pot. Add the remaining broth and 1 quart water. Bring to a boil; lower the heat and simmer gently until reduced to 3 cups, about 1-1/2 hours. Strain through a medium-mesh sieve into a 2-quart measuring cup; discard the solids.

Roast the turkey

• Uncover the turkey, discard the paper towels, and set the turkey on a V-rack in the roasting pan. Let sit for 1 hour at room temperature.
• Position a rack in the lower third of the oven and heat the oven to 350°F.
• Roast the turkey, basting occasionally after 1 hour and rotating the pan halfway through, until an instant-read thermometer inserted into the thickest part of the thigh registers 165°F, 2 to 2-1/2 hours. If the skin gets too dark during roasting, tent with foil.
• Tilt the turkey so the juice in the cavity runs into the roasting pan. Transfer the turkey to a platter or carving board. Remove the string, tent with foil, and let rest at room temperature for at least 30 minutes and up to 1 hour before carving and serving.

Make the gravy

• Pour the drippings from the turkey roasting pan into a fat separator and allow the fat to rise to the top. Transfer 1/4 cup of the fat to a 3- to 4-quart saucepan; discard the remaining fat and add the defatted drippings to the reserved broth in the measuring cup.
• Add the Madeira to the roasting pan and boil over medium-high heat, scraping up any browned bits from the bottom of the pan, until reduced to 1/2 cup, about 10 minutes. Strain through a medium-mesh sieve set over the measuring cup of broth.
• Add the reserved butter to the fat in the saucepan and melt over medium-high heat. Add the flour and cook, whisking constantly, until slightly thickened, 3 to 4 minutes. Slowly whisk in the broth mixture and bring to a boil; then turn the heat down and simmer vigorously, whisking occasionally, until the gravy is reduced to 4 cups, 8 to 16 minutes. Stir in the lemon juice and season to taste with salt and pepper.
• Carve the turkey and serve with the hot gravy.