Usually added to the mincer, the breast is one of the most underrated parts of the lamb - think the equivalent of pork belly. It's best cooked long and slow to render some of the fat, and stuffing it is the way to go.
Note Greek oregano, also known as rigani, is more aromatic than the dried oregano sold in supermarkets. It's available in dried bunches from Greek delicatessens. If unavailable, substitute dried oregano.