Cut the carrots and parsnips into 2 1/4 inch matchsticks. Toss them in a large bowl with olive oil and sprinkle with salt and pepper. Pour vegetables into a large pyrex baking dish or baking sheet so that they are mostly in a single layer.
Roast, stirring every 15 minutes, until they are tender and browned, about 40-45 minutes.
Mix together herb butter ingredients in a small bowl and stir well.
Remove carrots and parsnips from oven, and while still hot, toss with herb butter to coat well. Serve immediately.