Preheat a large (preferably) cast iron skillet to medium.
While the skillet is heating up, peel and chop the carrots and parsnips into bite-size pieces, discarding the ends.
When the pan is hot, add in the olive oil, carrots, and parsnips. Season with salt and pepper and toss until all of the veggies are coated.
Cover the pan and let cook, stirring every 15 minutes or so for about 45 minutes.
While the veggies cook, mix together the maple syrup, dijon mustard, and thyme in a small dish.
When the veggies are tender, turn off the heat and pour the sauce over the top. Stir until coated, then serve.