Place pistachios and garlic in a KitchenAid Food Processor; pulse until coarsely chopped. Add basil, lemon juice and salt; pulse until finely chopped. Continue processing while gradually adding oil in a steady stream. Add cheese; pulse just until blended.
Sprinkle lamb chops with salt and pepper. Heat oil in a large cast iron skillet over medium heat; add lamb. Cook until desired doneness (for medium-rare, a thermometer should read 135°; medium, 140°; medium-well, 145°), 2-3 minutes on each side. Serve with basil pesto and pomegranate seeds.
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