In a dutch oven or slow cooker bowl, combine rum, sugar, and 2 cups water.
Liberally salt the pork on all sides. Depending on size and how your roast is cut, you may need a little more than the recipe calls for. Do not skimp on salt.
Most pork shoulders have a “skin” of fat on one side. Place the roast in the dutch oven or slow cooker with the fat side up. (If there is none, either side up is fine. Fat side up means the meat will self-baste as it melts. You may wish to occasionally baste the meat if you do not have a fat layer, but it’s not strictly necessary.)
Add more water, if necessary, so that the liquid comes approximately halfway up the sides of the meat.
If cooking in an oven:
Cover dutch oven and place the pot in a cold oven. Turn oven on to 300F and bake for at least 5 hours, or until thermometer registers 160F. At this point, the roast can be sliced and served. Continue cooking for up to 3 hours more for pork that falls apart and shreds (perfect for using as filling for bbq, soft tacos, etc.) If you are in a hurry, cook meat until done and chop instead of shredding.
If cooking in a slow cooker:
Cover ceramic insert and place in cooker. Cook on high for 6 hours or low for 9. Meat is done when thermometer registers 160F. Remove and slice/serve, or leave in cooker for up to 4 hours more for meat that will shred itself.
It also can be frozen for later use. Place cut/shredded meat in a freezer safe container along with just enough cooking liquid to cover.
You could also use this to cook chicken parts.
You could use a light rum for this if that is all you have on hand, but light rums are generally more neutral in flavor, so you won’t get as much of a caramel/molasses undertone. Rum is distilled from sugar cane. Check carefully for any colors or other additives.
Instead of water, use apple cider or juice, if safe for your family.