Heat a cast-iron skillet over high heat for 2 minutes. While the skillet heats, pat the steaks dry with a paper towel, and then sprinkle with the chopped rosemary and some salt and pepper. Add the oil to the skillet and, once it shimmers and is almost smoking, add the steaks and rosemary sprig and sear for 4 minutes on each side, until well browned with a nice crust. Remove the steaks and rosemary sprig to a plate and loosely tent with foil.
While the steaks rest, lower the heat to medium, add the shallots and thyme to the skillet and cook until soft, about 2 minutes. Add the wine, turn the heat back up, and scrape up any browned bits that are stuck to the bottom of the skillet. Reduce the wine by half, about 3 minutes. Stir in the beef broth, blackberries and berry preserves. Mash the berries into the sauce with a wooden spoon. Continue simmering until the sauce is reduced and coats the back of a spoon. Remove from the heat and swirl in the cold butter. Taste for seasoning and add salt and pepper if needed.
Serve the steak drizzled with the sauce.