Combine the first 6 ingredients in a saucepan; bring to a boil, stirring until salt dissolves. Remove from heat; cool. Pour brine into a 2-gallon zip-top plastic bag. Add pork; seal. Refrigerate 8 hours or overnight, turning bag occasionally.
Preheat oven to 350°.
Bring 2 cups cider to a boil in a small saucepan over medium-high heat. Cook until cider has thickened and reduced to 1/4 cup (about 15 minutes). Set aside.
Remove pork from bag; discard brine. Place pork on rack of a broiler pan coated with cooking spray. Lightly coat pork with cooking spray. Combine rosemary, sage, and black pepper; sprinkle evenly over pork. Bake at 350° for 1 hour or until thermometer registers 155°, basting twice with cider reduction during final 20 minutes of cooking. Remove from oven; baste with remaining cider reduction. Let stand 10 minutes before slicing.