Add all ingredients for the pomegranate reduction sauce to a small skillet and bring to a full boil.
Allow mixture to boil, stirring occasionally, until the mixture has thickened and reduced to a third of its starting volume, about 30 to 40 minutes.
Pour pomegranate reduction into a small bowl or pitcher and set aside until ready to use.
Sear the Duck Breasts:
Preheat the oven to 350 degrees F.
Using a sharp knife, score the skin of the duck breasts with several lines going cross-wise at a 45-degree angle, creating deep diamonds in the skin. Note: Be careful not to cut too deep, as you don’t want to cut into the flesh of the meat.
Sprinkle both sides of the meat with salt and pepper.
Heat a cast iron skillet to medium-high and add just enough oil to coat the surface of the pan (about 2 tablespoons).
Once the skillet is completely hot, carefully place the duck breasts on the hot skillet skin-side down.
Cook duck breasts for 5 minutes, or until the skin has browned and turned crispy. Carefully flip to the other side and cook an additional 2 to 3 minutes.
Immediately remove the skillet from the heat, cover with aluminum foil, and place on the center wrack in the oven. Note: The skillet will be very hot, so be sure you use an oven mitt when handling it.
Bake for 5 minutes, then remove from the oven and immediately remove the aluminum foil.
Use tongs to place duck breasts on a cutting board.
Using a sharp knife, cut thin strips of duck diagonally. The duck should be medium-rare to medium*
Drizzle desired amount of pomegranate reduction sauce on the sliced duck breasts and serve with your favorite side dishes.
Notes
*For a rarer piece of meat, skip the oven process and serve immediately after searing the duck.