In a 2-gallon resealable plastic bag, combine the yogurt, olive oil, mint, 1 teaspoon salt and 1/2 teaspoon pepper. Add the lamb, turning to coat evenly, and refrigerate for 24 hours.
Preheat the oven to 350 degrees . Place the lamb fat side up in a roasting pan and roast until an instant-read thermometer inserted into the center registers 145 degrees for medium rare, about 1 1/2 hours. Let rest for 15 minutes before slicing.