Preheat your oven to 400°F (200°C).
Peel and dice the carrots and parsnips into 1-inch chunks, and halve the Brussels sprouts.
Toss the vegetables with olive oil, sea salt, and black pepper on a parchment-lined baking sheet.
Roast the vegetables for 20-25 minutes, tossing halfway through, until they are tender and caramelized.
While vegetables roast, place the duck leg skin-side down in a cold cast-iron skillet.
Turn the heat to medium and cook for 8-10 minutes without moving the duck to render the fat and achieve a deep golden, crispy skin.
Flip the duck leg and cook for an additional 2-3 minutes until heated through.
Plate the roasted root vegetables and place the crispy duck leg on top, garnishing with fresh thyme leaves.