Shoulder of lamb is quite fatty, but thatâs what makes the meat so sweet and succulent, and by cooking it for a long time at a low temperature, the meat becomes so tender it just falls off the bone. This is the perfect roast to put in the oven and leave while you are out as it cooks slowly in the oven and you will return to a house full of wonderful aromas and meltingly tender meat. Serve it with fresh mint sauce.