1. To prepare brine, combine first 6 ingredients, stirring well.
2. To prepare turkey, remove giblets and neck from turkey; reserve neck and giblets. Trim excess fat. Place a turkey-sized oven bag inside a second bag to form a double thickness. Place bags in a large stockpot. Place turkey inside inner bag. Add brine. Secure bags with several twist ties. Refrigerate 12 to 24 hours.
3. Preheat oven to 500°.
4. Remove turkey from bags; discard brine. Pat turkey dry. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Combine 1 tablespoon sugar and next 6 ingredients (through coriander) in a small bowl. Rub spice mixture under loosened skin over flesh. Place 1 apple quarter and 1 poblano quarter in the neck cavity; close skin flap. Arrange 5 apple quarters, 1 poblano quarter, and 1 cup cilantro leaves in the body cavity. Secure legs with kitchen twine. Arrange turkey, neck, and giblets on the rack of a roasting pan coated with cooking spray. Arrange remaining 6 apple quarters and 6 poblano quarters in bottom of roasting pan coated with cooking spray. Place rack with turkey in pan. Roast at 500° for 30 minutes.
5. Reduce oven temperature to 350° (do not remove turkey from oven). Place a foil tent over turkey breast. Pour 3 cups water in bottom of pan.
6. Bake turkey at 350° for 40 minutes. Rotate turkey, and baste with 3/4 cup broth. Roast for 30 minutes; rotate turkey. Baste with 3/4 cup broth. Roast 20 minutes or until a thermometer inserted in the thickest part of the thigh registers 165°. Remove from oven. Place turkey, breast side down, on a jelly-roll pan or cutting board. Let stand, covered, for 30 minutes. Serve breast side up. Chop giblets. Discard neck.
7. Strain pan drippings through a sieve into a bowl; discard solids. Melt butter in a large saucepan over medium-high heat. Add onion; sauté for 5 minutes or until translucent. Stir in reserved chopped giblets and garlic; sauté 2 minutes, stirring constantly. Weigh or lightly spoon flour into a dry measuring cup, and level with a knife. Sprinkle flour over onion mixture; saute 2 minutes, stirring frequently. Add drippings, remaining 1 1/2 cups broth, and 1 cup apple cider; bring to a boil. Reduce heat, and simmer until reduced to 3 cups (about 15 minutes). Strain through a sieve over a bowl, and discard solids. Stir in chopped cilantro and lime juice. Discard turkey skin; carve. Serve with gravy.