If you're thinking low, slow cooking and want that fall-apart, off the bone type of meat then look for lamb. It makes the perfect slow roast because it's gamey meat and will steal the show at your dinner table so do take a look at my lamb recipes.
Wonderful and unbelievable flavor in this Braised Lamb Shanks In Red Wine but you knew I was going to say that right? Ofcourse, it's lamb - lamb shanks! What a meal! Also this equally strong contender is my Slow Roast Leg of Lamb (bone-in).