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1
Season: In a small bowl, combine the paprika, brown sugar, dry mustard, sage, 1 tsp. salt, and 1 tsp. pepper. Set aside 2 tsp. to use in the braise and sprinkle the remaining rub all over the ribs. Cover and refrigerate for at least 2 hours but preferably overnight.
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2
SEAR: Prepare a gas grill for direct grilling over medium-high heat. Grill the ribs until nicely browned, 3 to 5 minutes per side. Transfer to a platter, let cool briefly, and then tie each rib with 3 or 4 loops of butcher's twine.
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3
BRAISE: Prepare the grill for indirect grilling. In an 8-quart heavy-duty pot, cook the bacon over medium heat, stirring occasionally, until it just starts to crisp, 2 to 3 minutes. Add the onions and cook, stirring occasionally, until soft and beginning to color, 6 to 8 minutes. Add the garlic, carrot, and the reserved spice rub and cook for about 1 minute more. Add the broth, beer, vinegar, bay leaves, and caraway seeds. Bring to a boil, reduce the heat, and simmer, uncovered, for 10 minutes.
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4
Nestle the ribs into the braising liquid. Set the pot on the grill over the cool zone. Cover the pot, close the grill lid, and cook until fork-tender, about 1-1/2 hours, turning the ribs halfway through cooking.
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5
Transfer the ribs to a tray. Strain the braising liquid into a heatproof vessel, such as a Pyrex measuring cup, and let sit until the fat rises to the top. Discard the solids. Skim off and discard the fat. Keep warm.