Heat oven to 350. Combine nutmeg, allspice, salt, and pepper in small bowl. Rub over all sides of pork.
Heat 1 tbsp of the butter and oil in large skillet over medium heat until butter is melted and oil is hot. Increase heat to medium high; cook pork in batches 3 to 4 minutes or until browned on all sides, adjusting heat if needed. Place on foil-lined rimmed baking sheet; reserve skillet (Pork can be made to this point 8 hrs in advance. Cover and refrigerate).
Combine Cider, rum and brown sugar in small bowl. Remove drippings from skillet. Heat skillet over high heat until hot. Pour in cider mixture. Boil until slightly thickened (bottom of skillet will show when stirring). Whisk in remaining 1 tbsp butter, bring to a boil, remove from heat.
Bake pork 10 minutes; increase oven temperature to 375. Brush pork with some of the cider glaze; bake an additional 10-15 minutes or until internal temperature reaches 140-145°F Cover loosely with foil; let stand 10 minutes.
Meanwhile, pour any pan juices into remaining glaze; boil 1 minute. Serve over pork.