Combine first 6 ingredients, stirring until sugar dissolves. Place pork in a large zip-top freezer bag; add cider mixture. Seal bag, and chill 24 hours.
Remove pork from brine, and pat dry with paper towels; discard brine. Heat oil in a large skillet over medium-high heat; add pork. Cook 6 minutes or until browned on all sides, turning meat occasionally. Place pork on a rack in a lightly greased shallow roasting pan.
Bake at 300° for 1 hour and 15 minutes or until a meat thermometer inserted into thickest portion registers 150°. Remove from oven; cover and let rest 10 minutes or until thermometer reaches 160° before slicing. Serve with Chestnut and Red Cabbage Sauté.