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.
Overnight brining tenderizes the roast. If the cider reduction becomes too thick to brush on the pork, warm it in a saucepan over low heat.