How to Make It
Combine sugar, peppercorns, bay leaves, 1½ cups of the cider and ¼ cup of the salt in a medium saucepan; bring to a boil over medium-high heat. Cook, stirring constantly, until sugar and salt have dissolved, about 2 minutes. Remove from heat; stir in ice and remaining 1½ cups cider. Place brine and pork in a 2-gallon ziplock plastic bag; seal bag and refrigerate for 8 to 24 hours.
Preheat oven to 425°F. Remove pork from brine and pat dry with paper towels. Discard brine. Finely chop leaves from 4 of the rosemary sprigs to measure 1 tablespoon. Combine rosemary leaves, fennel seeds and ½ teaspoon each of the salt and pepper in a small bowl; rub mixture all over pork.
Combine carrots, apples, fennel, onion and remaining 2 rosemary sprigs in a large bowl; drizzle with 3 tablespoons of the oil and sprinkle with remaining 1 teaspoon salt and ½ teaspoon pepper. Toss gently to coat. Spread in an even layer in a large roasting pan.
Heat remaining 1 tablespoon oil in a large skillet over mediumhigh heat. Add pork and cook, turning, until brown on all sides, about 10 minutes. Place on top of vegetables in roasting pan. Bake until a thermometer inserted into thickest portion of pork registers 145°F, about 30 minutes. Transfer pork to a cutting board; let stand for 15 minutes before slicing. Stir vegetables and return roasting pan to oven. Bake vegetables until tender and caramelized, about 15 minutes. Serve pork with vegetables and pan drippings, garnished with fennel fronds and additional rosemary sprigs.