Cut 4 to 5 slashes, about 1/4-inch deep, in a crosshatch pattern on both sides of the lamb.
Pour 1/2 tablespoon of olive oil into a bowl. Add black pepper, coriander, paprika, cayenne pepper, and kosher salt. Whisk together; add enough olive oil to make a paste. Rub lamb pieces into the spice mixture until thoroughly coated. Cover with plastic wrap and marinate in the refrigerator for at least 2 to 3 hours, or overnight.
Preheat an outdoor grill for medium heat and lightly oil the grate.
Place lamb on the grate. Grill to a doneness between medium and medium-well, about 8 minutes per side. An instant-read thermometer inserted into the center should read at least 140 degrees F (60 degrees C).
Transfer lamb to a plate and let cool, about 5 minutes. Slice thinly. Mix yogurt, mustard, garlic, and mint together; serve sauce with the lamb.