Preheat oven to 450°. Combine sweet potato, turnip wedges, carrot slices, maple syrup, and shallots with olive oil, garlic, 1/2 teaspoon black pepper, and 1/4 teaspoon salt. Arrange mixture in a 13 x 9inch glass baking dish. Bake at 450° for 40 minutes, stirring once. Sprinkle chicken with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Arrange chicken over vegetable mixture. Reduce oven temperature to 350°; bake at 350° for 20 minutes or until chicken is done. Let chicken stand 5 minutes; slice. Toss vegetable mixture with white balsamic vinegar. Shave Parmigiano-Reggiano cheese over mixture, and sprinkle with chopped fresh thyme.