Puree the garlic, paprika, coriander, cumin, 1 tablespoon salt and 1/2 teaspoon pepper into a paste in a mini food processor. Add the olives, parsley, cilantro and lemon juice; pulse to chop. Add the butter and pulse to incorporate all the ingredients.
Cut the lamb along a natural seam into 2 equal pieces. Rub the olive-spice mixture evenly all over the lamb; cover and refrigerate for 2 to 6 hours.
Bring the lamb to room temperature about 30 minutes before cooking. Preheat the broiler and line a broiler pan with foil. Place the lamb smooth-side down on the pan. Broil just until charred, about 15 minutes. Remove the pan from the oven; carefully turn the lamb, using tongs. Return to the oven; broil until a thermometer inserted into the thickest part of the meat reads 125 to 130 degrees, about 10 more minutes.
Transfer the lamb to a cutting board, cover loosely with foil and let rest for 10 minutes. Slice across the grain and arrange on a platter.