Combine pomegranate juice, molasses, garlic and rosemary in a medium saucepan. Bring to a boil over high heat. Reduce heat; simmer until mixture is reduced to 1/2 cup, about 15 minutes. Strain out and discard garlic and rosemary. Stir in 1 tablespoon of the butter and pomegranate seeds; let stand at room temperature.
Meanwhile, heat oven to 350°F. Melt 2 tablespoons of the butter; toss with rutabaga, oregano, brown sugar and 1/2 teaspoon of the salt. Spread into a single layer on a parchment lined 15x10-inch jelly roll pan or rimmed baking sheet. Bake 15 minutes. Season pork loin with 1-1/2 teaspoons of the salt and the pepper. Melt 2 tablespoons of the butter in a large ovenproof skillet over medium heat. Add pork; brown on all sides, about 5 minutes.
Transfer skillet with pork loin to oven alongside rutabagas. Continue to bake 16 to 18 minutes or until internal temperature of pork reaches 140°F and rutabaga is tender.
Transfer pork loin to carving board; tent with foil and let stand 5 minutes. Add Brussels sprouts to drippings in skillet; sauté over medium heat 5 minutes or until crisp-tender. Stir in remaining 1/2 teaspoon salt. Carve pork loin crosswise into 1/4-inch slices; serve with rutabagas, Brussels sprouts and pomegranate sauce.