1. Peel and trim carrots, leaving 1 1/2 inches of greens intact. Bring a large pot of water to a boil; add 1 tablespoon salt. Add carrots; cook until bright and just tender, 3 to 4 minutes. Immediately plunge into an ice-water bath. Drain.

2. Preheat oven to 375 degrees. Whisk together sugar, vinegar, honey, and peppercorns.

3. Heat oil in a large ovenproof skillet over medium-high heat. Add carrots, rosemary, and star anise; cook, stirring, until carrots are tender, about 5 minutes. Stir in honey mixture. Season with salt. Bring to a boil over medium-high heat, turning carrots to coat.

4. Transfer skillet to oven. Roast carrots until slightly caramelized, 20 to 25 minutes. Drizzle with oil, if desired.