Cook steaks in a 10-inch cast-iron skillet over medium heat for 2 minutes. Increase heat to medium-high. Add the steaks and cook 3-4 minutes per side for medium-rare. Transfer the steaks to an ovenproof dish and place in a 200 degree oven. (I include this because the recipe talked about how to cook the steaks, but I'm only interested in the sauce.).
Return the skillet to medium heat and add 1 tsp oil and the shallot. Saute until the shallot has softened, about 1 minute. Add the wine and cook for one minute. Add pomegranate juice and the stock, then bring to a simmer and cook until reduced to 1/3 cup. Add cornstarch mixed with water, then cook until thickened.
Spoon the sauce over the filets and serve (garnished with freshly chopped chives and pomegranate seeds, if desired).