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Cut the meat and fat into pieces that will fit in your grinder. Mix all the salts and spices with the meat and fat. Put everything in the freezer for 1 hour to chill. Meanwhile, take out about 20 feet of sheep casings and soak them in tepid water.
Grind the mixture in the fine die of your grinder, making sure everything stays cold. If the meat warms beyond 35°F, stop and freeze everything for 30 minutes to cool it down. Put the ground meat in the fridge while you clean up.
Using a Kitchenaid or other stand mixer, or your (very clean) hands, add the ice water and mix the meat and fat -- use the lowest setting on a stand mixer -- until it binds, about 1 to 2 minutes. Again, put the meat in the fridge while you clean up.
Flush the sheep casings with warm water and set aside.
Put the meat mixture in your sausage stuffer and stuff into the sheep casings. Remember that sheep casings are weaker than hog casings, so you do not want to overstuff them. As you are stuffing, fill up a link between 12 inches and 24 inches, leaving plenty of extra casing on either end. Cut the casing and continue to make these large links until you've used all the meat.
Use a sterilized needle to pierce the casings wherever there are air pockets. Gently squeeze the meat in the casings to tighten. You may break some until you get the hang of it. If you do, put the meat back into the stuffer and make another link. Once all the links are firm in their casings, tie the ends together in a double or triple knot. Trim any excess casing.
Hang the links to dry in a cool place for several hours, depending on how warm it is. If the temperature is 70°F or above, hang for only an hour.
Move the links to a smoker and smoke until the interior of the meat hits 150° -- keep your smoker cool enough so that this takes about 4 hours. You want the links to get lots of smoke time.
Let the links cool, then move to a place to hang them. Ideally this place is between 35°F and 60°F and dark. Hang the links for 3 to 5 days to let them dry out a bit. They are now reasonably shelf stable, but I keep them in the fridge. If for some reason you plan on keeping them more than a month or so, wrap tightly (or vacuum seal) and freeze.