Cut parsnip, leek, and carrot into short strips. Cut onion coarsely. Leave garlic cloves whole or cut in half. Do not peel the garlic.
Evenly coat the vegetables in the oil and thyme. Spread evenly in a pan and roast for 60 - 90 minutes at 400 degrees. Stir occasionally to avoid sticking to the bottom. Vegetables are done when parsnips and carrots are tender and the edges of the leeks are burnt.
Finally, drizzle balsamic vinegar to taste over vegetables, stir, and serve.