Set rack about 6 inches from heat and preheat broiler.
In a small bowl stir together cardamom, salt, and pepper to taste. Let lamb stand at room temperature 30 minutes.
Pat lamb dry with paper towels and rub both sides with cardamom mixture. Broil lamb on rack of a broiler pan 14 minutes on each side for medium-rare. Transfer lamb to a cutting board and let stand 10 minutes.
In a bowl whisk together pesto, vinegar, yogurt, and 2 tablespoons hot water, adding additional hot water if necessary to reach desired consistency.
Carve lamb against grain into 1/2-inch-thick slices and serve with pesto.
