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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.