Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Peel the carrot and parsnip, then cut them into 1-inch chunks; halve the radishes.
Place the vegetables on the baking sheet and toss with sea salt, black pepper, and fresh thyme, using a small amount of the rendered fat from the duck packaging to coat.
Roast the vegetables for 20-25 minutes, tossing halfway through, until they are tender and caramelized.
While the vegetables roast, place the duck leg skin-side down in a cold non-stick skillet.
Turn the heat to medium and sear for 8-10 minutes without moving it, allowing the fat to render and the skin to become deeply golden and crispy.
Flip the duck leg and cook for an additional 2-3 minutes until heated through to the center.
Drizzle the balsamic vinegar over the roasted vegetables and serve immediately alongside the crispy duck leg.