Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Peel and slice the carrots and parsnips into uniform half-moons.
Toss the vegetables on the baking sheet with olive oil, sea salt, and black pepper until evenly coated.
Roast the root vegetables for 20-25 minutes, tossing halfway through, until they are tender and slightly 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 approximately 10 minutes.
Once the skin is golden and shatteringly crisp, flip the leg and cook for an additional 3 minutes to ensure it is heated through.
Arrange the roasted vegetables on a plate, top with the crispy duck leg, and garnish with fresh thyme and a drizzle of balsamic vinegar.