In a large bowl or pan (at least 8 qt.), combine 4 quarts water, kosher salt, and 3/4 cup sugar. Stir until salt and sugar are dissolved. Rinse turkey and trim off back, ribs, wing meat, and excess neck skin if attached. Submerge turkey in brine, cover, and chill, turning turkey occasionally, at least 12 hours or up to 24 (see notes).
Lift turkey from brine, rinse well, and pat dry; discard brine. Set turkey, skin up, on a rack in a 10- by 15-inch roasting pan. Brush skin with melted butter.
Bake in a 375° regular or convection oven until a thermometer inserted through thickest part of breast to bone registers 160°, 1 1/4 to 1 1/2 hours.
Meanwhile, put remaining 1/4 cup sugar in an 8- to 10-inch frying pan over high heat; shake pan often until sugar is amber-colored, 2 to 3 minutes. Add 3/4 cup broth and the cranberry concentrate; stir over medium-high heat until blended, 1 to 2 minutes. Remove from heat.
Transfer turkey to a platter or board; let rest in a warm place about 10 minutes. Add remaining 3/4 cup broth to roasting pan and stir to free browned bits. Pour drippings through a fine strainer into cranberry mixture. Add any juices accumulated on platter from turkey. Stir over high heat until boiling. Remove from heat and skim off and discard any fat. Add lemon juice and salt and pepper to taste. Pour into a gravy boat.
Slice turkey and serve with cranberry pan juices to add to taste.
I ended up following recipe for brining but I cooked it in a turkey bag at 350. It was extremely moist and perfectly flavored. I was not a fan of the jus but my husband and I decided that we are just partial to good ole fashioned turkey gravy.
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