Whisk together the light brown sugar, coffee, sea salt, red pepper flakes, ginger and paprika in a small bowl. Put the pork in a large glass baking dish and rub it all over with the spice mix. Cover the dish with plastic wrap and refrigerate for at least 12 hours and up to 18 hours.
Remove the pork from the refrigerator 15 minutes before roasting. Preheat the oven to 250 degrees F. Put the onions, sauerkraut and its juices and pumpkin puree in a large roasting pan and stir to combine. Put the pork shoulder on top. Pour any juices and spices from the glass baking dish over the meat. Roast for 2 1/2 hours.
Pour the apple cider around the pork and cook until a meat thermometer inserted into the thickest part of the shoulder registers 145 degrees F., about 2 1/2 hours more. At this point, a rich crust should have formed on the meat, the pork will almost be falling off the bone and the pumpkin-sauerkraut mixture in the bottom of the pan will be a deep, caramelized orange.
Cover the roasting pan loosely with foil and let the pork rest for 30 minutes. Transfer the pork to a cutting board to carve, and serve slices of the pork on top of the pumpkin sauerkraut.
Pair this delicious pork with Starbucks VIA® Instant coffee.