Preheat your oven to 400 °F (200°C) and line a baking sheet with parchment paper.
Peel the carrots and parsnips, then slice them into 1/2-inch thick rounds.
In a bowl, toss the sliced vegetables with olive oil, minced garlic, fresh thyme leaves, and half of the sea salt and black pepper.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 20-25 minutes, flipping halfway through, until tender and caramelized.
While the vegetables roast, place the duck leg skin-side down in a cold cast-iron skillet.
Turn the heat to medium-low to slowly render the fat and crisp the skin for about 8-10 minutes without moving the leg.
Once the skin is golden and very crispy, flip the duck leg and cook for an additional 2-3 minutes to ensure it is heated through.
Season the duck with the remaining sea salt and black pepper, then serve immediately over the roasted root vegetables.