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Marinate and roast ribs:
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Mince and mash garlic to a paste. Stir together with rosemary and thyme, brown sugar, vinegar, cayenne and salt. Rub evenly all over ribs and transfer to roasting pans. Marinate, chilled, 8 to 24 hours.
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Preheat oven to 425u00b0F with racks in upper and lower thirds.
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Pour 1 cup water into roasting pan and tightly cover pan with foil. Roast ribs, rotating position of pan halfway through, until meat is very tender, about 1 3/4 hours. Remove pan from oven and transfer ribs to a platter or leaved covered.
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Make glaze:
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To make the glaze, combine all of the ingredients in a large pot on medium-low heat. Allow to simmer, stirring every so often, for a few hours, until the sauce is nice and thick. Set aside.
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Prepare grill for direct-heat cooking over medium-hot charcoal (medium heat for gas)
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Brush some of glaze onto both sides of racks of ribs. Grill, turning occasionally, until ribs are hot and grill marks appear, about 6 minutes.
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Brush ribs with more glaze and serve remaining glaze on the side.
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To bring the ribs and glaze together, do the following. Turn on the broiler (if you don't have a broiler, get the oven up to 450u00b0F). Cut the rib racks into individual ribs, place them on a foil-lined cookie sheet or broiler tray, and brush them aggressively with the glaze. Pop them under the broiler and watch them carefully: all that sugar makes them burn very easily! You want the glaze to fuse with the ribs; it takes 8 to 10 minutes. Serve the ribs hot with lots of napkins-trust me, you'll need them.
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Cooks' notes:
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Ribs can be roasted and glaze can be made 1 day ahead and chilled separately (covered once cool). Bring to room temperature, about 30 minutes, before glazing and grilling.
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Ribs can be broiled 3 to 4 inches from heat (instead of grilled) about 8 minutes.