jlawrence01 wrote:Why not cook them pretty much the same as lamb shanks? I cannot believe that the taste would be that different.
Well, except one tastes like goat, and the other tastes like lamb

Actually, I cook lamb shanks fairly often (at least in the winter), usually in wine or some kind of lemon-herb broth. Indeed, either method would probably work fine for goat shanks too, but I was just looking for some recipes designed specifically for goat. The goat shanks are much leaner than lamb shanks, with very little fat. That is probably good, since braised lamb shanks can be pretty greasy.
I like Michael's idea of a pseudo-birria. At least the chile and garlic (and maybe some thyme?) marinade seems like a good place to start. I think I will forgo the masa seal though, and stick to putting foil under the cover.
I have done lamb shanks fairly successfully in a pressure cooker, but they lacked the deep caramelized tones that come with slow-braising. In that case, finishing them up in a broiler makes perfect sense. I am not sure that goat is fatty enough to hold up to pressure-cooking.