Place the pomegranate juice in a medium, heavy-bottomed pan over medium heat. Bring to a lively simmer and reduce until the juice is thickened to a syrup, and has reduced by about two-thirds, which will take about 10 minutes. Check the juice frequently to be sure it isn’t reducing too much. When the juice has reduced, remove it from the heat, and reserve.

Heat a heavy skillet over medium heat. When it is hot but not smoking, place the duck breast in it, skin side down. Cover and cook it until the skin is deep golden, about 8 minutes. Flip the duck breast onto the meat side, then flip it immediately back onto the skin side and continue cooking 3 to 4 minutes.

Remove the duck breasts from the pan, and place them on a cutting board that will catch any juices that run from them. Season the duck breasts with salt and pepper and let rest for about 5 minutes.

To make the sauce, reheat the reduced pomegranate juice over low heat. Quickly whisk in the butter piece by piece, working on and off the heat so that it emulsifies into the pomegranate juice without melting, and thickens it slightly. Keep the sauce warm.

To serve, slice the duck breasts on the bias into ¼-inch thick slices, and arrange them in a rosette pattern just off-center on 6 to 8 warm dinner plates. Drizzle the duck with the pomegranate syrup, and drizzle the syrup around the edge of the plates, as well. Garnish with herbs, and serve immediately.