Toast both the 1 tablespoon and the 1/2 teaspoon cumin seeds (see Mojo) in a small saute pan over high heat until fragrant, about 30 seconds. Grind the seeds in a spice grinder or with a mortar and pestle and reserve 1/2 teaspoon for the Mojo. Mix remaining cumin with garlic, lime juice, olive oil, salt, oregano, and black pepper. Remove the pork loin from the ribs and chine bone by cutting between the meat and the bones. Rub the marinade all over loin and ribs. Place the loin back onto the ribs where it was removed and tie together with butcher's twine. Place in a nonreactive container, cover, and refrigerate for 4 hours or overnight.
Meanwhile, make the Mojo and reserve 3/4 cup to serve with the pork.
Prepare an outdoor grill with a medium-high fire for indirect grilling. Position a drip pan under grate on the cooler side of the grill. Set the roast rib side down over the pan on the side opposite from the heat. Cover, with the vent holes over the pork and cook, basting the meat periodically with the sauce. Rotate the roast 180 degrees after 30 minutes so it cooks evenly. (Add coals to the fire as needed to maintain an even heat.) After an hour, begin to baste with Mojo every 15 minutes and set the roast on its chine (back) bone, with the fat facing the heat, so it browns evenly. Cook until a meat thermometer inserted into the center of the loin registers 140 degrees F, about 1 1/2 hours in all.
Remove the roast from grill, cut the twine, and let the loin rest for 10 minutes. Meanwhile, place the ribs on the grill over direct heat with the side where the loin was attached facing down. Grill, turning as needed, until evenly browned, about 4 minutes. Let rest 5 minutes and cut between the ribs. Serve ribs with sliced loin and reserved Mojo.
Heat the reserved cumin in a skillet along with the garlic and olive oil. Cook over medium-high heat until garlic begins to sizzle, about 2 minutes. Remove from heat, transfer to a nonreactive bowl, and stir in remaining ingredients.
From Food Network Kitchens Get Grilling, Meredith 2005
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