How to Make It
Preheat oven to 400°F. Bring juice, honey, and vinegar to a boil in a small saucepan over high, stirring occasionally. Reduce heat to medium, and simmer until reduced to 1/2 cup, 12 to 15 minutes. Remove from heat. Stir in 1/2 teaspoon of the pepper.
Toss together squash, thyme, 2 tablespoons of the olive oil, and 1/2 teaspoon each of the salt and pepper on a baking sheet; spread in an even layer. Roast until caramelized and tender, about 20 minutes.
Meanwhile, heat remaining 2 tablespoons oil in a large ovenproof skillet over medium. Sprinkle turkey with remaining 1 teaspoon salt and 1/2 teaspoon pepper. Place turkey, skin side down, in skillet. Cook until golden brown, 8 to 10 minutes. Turn turkey breast, and transfer skillet to oven. Roast at 400°F for 10 minutes. Brush turkey with 2 tablespoons of the pomegranate mixture, and continue to roast until a thermometer inserted in thickest portion of turkey registers 160°F, 10 to 15 minutes, brushing turkey every 2 minutes with pomegranate mixture. Remove from oven, and let stand 10 minutes.
Transfer squash to a platter. Slice turkey across the grain, and place on platter with squash. Serve with remaining pomegranate glaze. Sprinkle with pomegranate arils and parsley.