Position one rack in center and one rack in bottom third of oven and preheat to 400 degrees F. Line two rimmed baking sheets with foil and set aside.
Peel the carrots and parsnips and then cut them in half lengthwise and crosswise to form sticks. (If the carrots or parsnips are bigger than specified, quarter or cut so that all of the pieces are about 1/2 to 3/4 inches thick.)
Place the carrots and parsnips in a large bowl, and sprinkle generously with salt and pepper. Drizzle 3 tablespoons oil over vegetables, and toss to coat. Divide the carrots and parsnips between prepared sheets, spreading them into an even layer.
Roast the vegetables for 10 minutes; stir. Roast for 10 minutes longer, stir, and reverse the sheets. Continue roasting until the vegetables are tender and nicely golden in places, about 15 minutes longer. (Can be prepared 2 hours ahead. Tent with foil and let stand at room temperature. Rewarm, uncovered, in 350°F oven for 10 minutes.)
Melt the butter in heavy small saucepan over medium heat. Stir in the honey and vinegar. Bring to a simmer and cook, stirring constantly, for about a minute or just long enough to thicken the mixture slightly.
Transfer the vegetables to a bowl, drizzle with the honey glaze, and toss to evenly coat.