Combine cider, salt, and 1/2 cup chopped sage, stirring until salt dissolves. Place pork in an extra-large zip-top plastic freezer bag; add cider mixture. Seal bag; chill 12 to 24 hours.
Remove pork from brine, and pat dry with paper towels. Sprinkle pork with pepper. Heat oil in a large skillet over medium-high heat; add pork. Cook 6 minutes or until browned on all sides, turning pork occasionally. Place pork on a rack in a lightly greased roasting pan. Sprinkle remaining 3 Tbsp. sage over pork.
Bake, uncovered, at 350° for 1 hour to 1 hour and 25 minutes or until a meat thermometer inserted into thickest part of roast registers 150°. Remove from oven; cover and let rest 10 minutes or until thermometer reaches 160° before slicing. Garnish platter, if desired. Serve with Sage and Pecan Pesto.