Preheat oven to 220°C Line a large roasting pan with baking paper. Remove core from parsnip (if woody) and cut into similar sized chunks to swede and turnip. Spread vegetables in a single layer in roasting pan.
Make balsamic glaze: Place oil, maple syrup, vinegar, garlic and salt and pepper in a screw-top jar. Secure lid and shake to combine. Heat a frying pan over medium-high heat. Add glaze and cook, stirring occasionally, for 5 minutes or until hot.
Pour glaze over vegetables and toss gently to coat. Roast vegetables, turning once, for 1 hour or until tender. Season with salt and pepper and serve with roast, grilled or pan-fried meat.