Position oven racks in the upper and lower third of the oven, put 2 baking sheets in the oven and preheat to 425 degrees F.
Cut all the vegetables into evenly sized 1 1/2-inch chunks. Cut out the core of the parsnips if they are tough and woody. Toss all the vegetables with the garlic, oil, 1 1/2 teaspoons salt and a generous grinding of pepper in a large bowl.
Carefully remove the hot baking sheets from the oven and drizzle with oil. Divide the vegetables evenly between the 2 pans and spread into a single layer. Roast the vegetables until tender and golden brown, stirring occasionally, 45 minutes to 1 hour. Toss with the parsley and chives.
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