Preheat the oven to 325 degrees F. Bring a large pot of water to a boil. Place the first 8 ingredients in a bowl and toss to combine. Arrange the carrot/parsnip mixture in a large, shallow baking dish. Cover with foil and bake 25 minutes.
Meanwhile, plunge the broccoli into the boiling water and cook 1 minute. Drain well, cool in ice-cold water, drain well again, and reserve.
When the carrots and parsnips have roasted 25 minutes, uncover and mix in the broccoli. Roast, uncovered, 20 minutes more, or until vegetables are tender and nicely coloured. Spoon the vegetables into a serving dish. Drizzle with the vinegar and 1 Tbsp. olive oil and serve.