What breed, what age and what sex is your mutton?
In my experience, older wethers, above say 4, of the non-primitive breeds can be quite fatty, which I don't like, so any recipes would involve either cutting it off or including some fast cooking time in with slow cooking to burn off some of the fat.
If it's cull ewes then they are likely to be older and scrawnier and need really slow cooking, in a covered dish with plenty of herbs and some red wine. Garlic can be good although I don't like garlic with sheep meat - love it with everything else.
If they are younger primitive wethers or hoggets then a long slow roast in a covered vessel, with plenty of Herbes de Provence and maybe rosemary, a dash of red wine and a final hot burst with the lid off to crisp the outside should be perfect. Sometimes I turn my oven off partway through the cooking time, especially if I am using a Le Creuset roaster, to allow a bit of thorough really slow cooking to go on. I started this when I would take various roast joints across to my son's, so the meat travelled in a hay box then had a hot blast on arrival - this makes the meat so tender and it falls off the bone.
What you don't want with mutton is short rapid cooking and red blood visible inside - it will be tough.
I nearly always serve roast hogget with mint sauce, or sometimes redcurrant jelly when it's cold the next day.
For shoulder, I would get it back boned but unrolled from the butcher, then stuff it and roll it myself, using ordinary white kitchen string to tie the roll. The choices for stuffing are many - a simple packeted herb stuffing is fine, or you can make your own with north African herbs and spices, or some local fruit such as cranberries or redcurrants, or a hot chillie mix. If the meat is at all fatty you need something like lemon or pineapple to cut through it. I don't use mint for stuffing, or for making sausages or burgers, as I find it becomes disappointingly flavourless, even a large amount fresh from the garden. Don't overstuff the roll as it will squeeze out at the ends.
I often find hot shoulder unsatisfactory as it falls to bits and you can see too much structure, so sometimes I cook the rolled shoulder then leave it to cool and eat it cold the following day when it's much nicer and holds together well.