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Place 1 quart of the water in saucepan over medium heat. Add the salt and sugar and stir until dissolved. Add the cloves, allspice, peppercorns and cinnamon stick. Remove from the heat and allow to cool completely, 30 minutes.
Combine the cooled sugar-salt mixture with the remaining 4 quarts of water and apple cider in a very large stockpot or food-safe plastic container. Add the rosemary. Submerge the turkey breast in the brine, cover and refrigerate for 4 to 5 hours.
Remove the turkey from the brine, rinse under cold running water and pat dry thoroughly. Position a rack in the center of the oven and preheat to 450°F.
Combine the salt, pepper, rosemary and thyme in a small bowl. Sprinkle some in the cavity of the turkey breast, then set the breast upright. Using your hands, rub the softened butter all over the skin, then sprinkle on the balance of the seasoning mix. Place the turkey on a rack inside a roasting pan. Add chicken broth to 1/4-inch depth in the bottom of the pan. This will prevent the drippings from burning.
Place the turkey breast in the oven and roast for 15 minutes. Turn the pan 180° and roast 15 minutes longer. Reduce the heat to 325° and continue roasting until the internal temperature at the thickest part of the breast registers 160°F, 35 to 45 minutes longer. If you feel the skin is browning too quickly during roasting, tent with heavy-duty aluminum foil.
Remove the breast from the oven and allow to rest for 20 minutes before carving.
While the turkey is resting, skim any excess fat from the pan juices and add enough chicken broth to equal 2-1/2 cups. Stir in the apple cider, place in a saucepan and bring to a simmer over medium heat. In a small bowl, whisk together 1/4 cup cornstarch with 1/3 cup water. Add to the simmering broth and continue whisking until thickened. Season to taste with salt and freshly ground black pepper. Transfer to a bowl or gravy boat for serving.