Heat oven to 425°F. In large bowl, place carrots, parsnips, and half each of the oil, chopped thyme, salt and pepper; toss to coat vegetables. In ungreased 15x10x1-inch pan, spread mixture in single layer. Bake 15 minutes.
Meanwhile, in same large bowl, toss squash with remaining oil, chopped thyme, salt and pepper. Add to pan; stir to combine vegetables.
Bake 35 to 40 minutes longer, turning vegetables twice with pancake turner, until vegetables are tender. Spoon into serving bowl or on platter; garnish with thyme sprigs.