In a 3-quart saucepan, bring 4 cups of the water, salt, brown sugar, peppercorns, bay leaves, and garlic to a simmer, stirring until the salt and sugar dissolve.

Cool the mixture completely.

Set a large turkey brining bag in an 18x13-inch rimmed baking sheet and pour in the cooled mixture.

Add the remaining 20 cups water and the apple cider, then stir.

Refrigerate until the brine is 40°F or colder.

Place the turkey in the chilled brine, press out excess air, and seal the bag.

Refrigerate at 40°F or colder for 12 to 18 hours, turning the bag once halfway through.

Remove the turkey and discard the brine without rinsing the turkey.

Pat the turkey very dry, then set it breast-side up on a rack in a 16x13-inch roasting pan.

Refrigerate uncovered for 8 to 12 hours.

Preheat the oven to 325°F with a rack in the lower third.

Let the turkey sit out for no more than 30 minutes while the oven heats.

Rub the vegetable oil over the turkey skin and under the breast skin.

Loosely fill the cavity with the onion, lemon, and sage sprigs.

Roast for 2 1/2 hours.

In a small saucepan, melt the maple syrup, butter, Dijon mustard, chopped sage, and black pepper over medium-low heat, stirring until combined.

Brush about one-third of the glaze over the turkey.

Apply the remaining glaze in two more coats 15 minutes apart.

Roast for 45 to 75 minutes longer, until an instant-read thermometer reads 165°F in the thickest part of the breast and the innermost part of the thigh, tenting loosely with foil if the skin gets too dark.

Transfer the turkey to a cutting board and tent loosely with foil.

Rest for 30 minutes before carving.