I'm with luvcookbooks on the untying, retying and stuffing. Tying up a piece of shoulder is pretty damn easy once you've seen it done; but keep your seams straight. Duxelles sound damn good in there, but I think capers and chevre would also work. Don't lose the fat as it's great stuff and will help crisp up the outside should you roast instead of braise.

Lamb shoulder is so delicious braised. You can untie it, stuff it, and tie it up again, but leave the fat because it's a tough meat and the fat helps tenderize it. You can skim it off, as above, after cooking. Recently, I've been pouring the cooking liquid hot into a measuring cup (clear) and able to spoon off the fat easily. If you are feeling ambitious, Julia Child has a great recipe for Braised Stuffed Shoulder of Lamb with Spinach and Mushroom Duxelles that I made for my first grown up dinner party when I was 18. The dish was great, although my life was a disaster that year...

Ok, I got lazy and didn't really trim any of the fat. Just finished dinner and oh my god, so good, tasted like carnitas. But as per these suggestions, I'll skim the fat tomorrow after it's been in the fridge all night.

Yum. Lamb yields fairly tender meat from all parts of its body, which means that, unlike beef and sometimes pork, most lamb cuts can be cooked using dry heat, including the shoulder.

The shoulder can be roasted if it's rolled and tied into a cylinder, and it can be stuffed, as well. If you'd prefer to roast it stuffed or unstuffed, I'd leave a good half-inch layer of fat around the roast and re-tie it. Lamb fat is "good" fat: only 36% of it is saturated, and the rest is poly- and mono-unsaturated fat, but it's not like you're going to drink the stuff anyway. Or are you. . .

If you decide to braise it, however, I'd trim off enough fat to leave a layer only 1/8"-1/4" thick. Any fat that melts into the braising liquid can be easily skimmed after cooking.

Usually a roast is tied to help it retain a shape which will allow it to cook evenly. I cut the twine to open the meat up so that I can rub it with herbs, spices, garlic... whatever flavors I'm shooting for. It sounds like there is a lot of extra fat. I would trim off some of it, but definitely leave some also, for flavor and moisture. Before cooking, tie the roast back up for even cooking. You can put veggies (choose your favorites... potatoes, carrots, onions, garlic cloves, fennel, for example) under the roast while you are cooking it to absorb fat and flavor.

If you braise properly, the fat will melt away and you can skim it later. If you braise at too high a heat, the fat will not melt away. I would leave the fat and follow the mantra, "low and slow is the way to go"