Preheat oven to 425 F for convection or 450 F for regular oven. Peel turnips with knife, then cut into pieces about 1 inch square. Whisk together olive oil and balsamic vinegar and toss with turnips, then spread in single layer in roasting pan. Roast turnips 25-30 minutes, or until slightly browned and softened.
Remove turnips from oven and place into serving bowl. Toss with additional 1 tsp. balsamic vinegar, season to taste with salt and freshly ground pepper, and serve immediately.