Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Peel and dice the carrots, parsnips, and turnips into uniform half-inch cubes to ensure they cook at the same rate.
In a medium bowl, toss the diced root vegetables with the duck fat, sea salt, and black pepper until every piece is lightly coated.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 20 to 25 minutes, tossing once, until tender and golden brown.
While the vegetables are roasting, place the duck leg skin-side down in a cold cast-iron or heavy-bottomed skillet.
Place the skillet over medium heat and cook for 8 to 10 minutes without moving it, allowing the skin to render its fat and become deeply golden and crispy.
Carefully flip the duck leg and cook for an additional 2 to 3 minutes on the flesh side just until heated through.
Remove the roasted vegetables from the oven and immediately toss them with the fresh thyme leaves and a drizzle of balsamic vinegar for acidity.
Plate the caramelized root vegetables and top with the crispy duck leg, serving immediately while the skin is at its peak texture.