Preheat the oven to 350 degrees F.
Peel the carrots and parsnips and cut them in half lengthwise, larger ones can be quartered. Place them on a large rimmed baking sheet.
Drizzle the carrots and parsnips with the olive oil and honey. Season with salt and pepper and toss to coat. Scatter the thyme sprigs on top. Place them in the preheated oven.
After 10 minutes, give the veggies a toss and put back in the oven for another 10 minutes until the vegetables are soft and slightly caramelized. Serve warm.