Malt-Beer-Brined Turkey with Malt Glaze

INGREDIENTS

• 1 unpeeled head of garlic, cut crosswise in half
• 2 peeled onions, quartered
• 3 tablespoons extra-virgin olive oil
• 2 tablespoons (1/4 stick) unsalted butter
• 1 bunch fresh sage
• 1 1/2 cups barley malt syrup
• 1/4 cup malt vinegar or apple cider vinegar
• 6 fresh sage sprigs
• 2/3 cup barley malt syrup
• 2 celery stalks, cut into chunks
• 4 fresh thyme sprigs
• 4 quarts water
• 3 12-ounce bottles stout beer (such as Guinness)
• 1/2 teaspoon ground black pepper
• 2 teaspoons ground black pepper
• 1 14- to 16-pound turkey
• 1 bunch fresh thyme
• 2 cups Diamond Crystal coarse kosher salt or 1 1/2 cups Morton coarse kosher salt
• 2 cups (or more) water