How to Make It
Preheat the oven to 400°. On 2 large rimmed baking sheets, toss the carrots with the olive oil, coriander and cumin. Season with salt and pepper and roast for about 25 minutes, until crisp-tender; keep warm. Leave the oven on.
In a skillet, toast the coriander, cinnamon, star anise and cumin over moderate heat, shaking the skillet, until fragrant, 2 minutes. Transfer the spices to a grinder and let cool, then grind to a powder.
Season the duck breasts with salt and pepper and rub all over with the spice mix. Heat a large cast-iron skillet. Add the duck, skin side down. Cook over moderate heat, spooning off the fat, until golden and just crisp, about 7 minutes. Turn the duck skin side up. Transfer the skillet to the oven and roast the duck for about 7 minutes, until medium-rare within. Transfer the duck breasts to a carving board and let rest for 5 minutes. Thinly slice crosswise and serve with the carrots.