Preheat your oven to 400°F (200°C).
Peel and slice the carrots and parsnips into 1-inch thick rounds.
Toss the vegetables with duck fat, sea salt, and black pepper on a rimmed baking sheet.
Roast the vegetables for 20-25 minutes, flipping halfway through, until they are golden brown and tender.
While the vegetables roast, place the duck leg skin-side down in a cold cast-iron or heavy-bottomed skillet.
Turn the heat to medium-low to slowly render the fat and crisp the skin for about 8-10 minutes.
Add the smashed garlic clove and thyme sprig to the pan during the last 2 minutes of searing, spooning the hot fat over the duck.
Flip the duck leg and cook for an additional 2 minutes on the flesh side until heated through.
Plate the crispy duck leg alongside the roasted root vegetables and serve immediately.