Score the skin of the duck breasts in a cross-hatch pattern to expose the fat underneath, making sure you don’t cut into the meat. Season with salt and pepper to taste.

Heat a large sauté pan over medium-low heat, and lay the breasts in the pan, skin side down. Allow to slowly cook until the fat has rendered, and the skin is golden brown and crisp, about 15 minutes. Tip: If a lot of fat starts pooling in the sauté pan, pour all but 2 tablespoons of the fat from the pan. Repeat this step as needed. Save this fat for the next time you sauté potatoes!

Once the skin is brown and crispy, flip the duck breasts over and add the thyme sprigs. Tilting the pan, baste the duck breasts with the thyme-infused fat for 1 to 2 minutes or until the duck is medium to medium rare, 125° to 130° on a meat thermometer. Transfer the duck to a cutting board with a juice groove, cover with foil to keep warm, and set aside.

While the duck is cooking, prepare the sauce. Bring the sugar and water to a boil in a heavy saucepan, and cook until the mixture is a golden caramel color.

Remove the pan from the heat, and carefully add the vinegar. Add the shallot, and swirl the pan over low heat until the caramel has dissolved, about 1 minute.

Stir in the chicken stock, orange juice and zest. Bring to a boil and reduce the heat to a simmer. Cook until the sauce is a nappé consistency.

Gently stir in the orange segments, and season with salt and pepper to taste.

Cut the rested duck breasts into 1/2-inch slices and fan out on a plate. Top with the sauce a few of the segments.