In a medium sized bowl, stir together the brine ingredients until the salt and brown sugar are dissolved. Place the loin in the brine and refrigerate covered for 6-8 hours.
Remove the pork loin from the brine and pat dry with paper towels. Bring to room temperature and sprinkle evenly with sea salt. Heat the grill until very hot and there is a nice bed of coals. Grill the pluma 2-3 minutes on each side for medium-rare. (Watch out for grease fires, which are common with a cut like this.) When done to your liking, let the pluma rest for 10 minutes before slicing.
While the pork is resting, make the sauce. In a sauté pan over medium heat, melt the butter and sauté the shallots for 2-3 minutes, or until translucent. Add the cherries, brown sugar, red wine, sherry vinegar, salt, pepper and thyme to the pan. Simmer for about 5-10 minutes, or until the liquid is reduced by half and desired sauce-like consistency. Slice the pork loin and top with the cherry sauce before serving.
Serve with Spanish potatoes au gratin, crusty bread and Spanish red wine like a Rioja or Tempranillo.