Season the steaks generously with salt and set aside at room temperature for about half an hour.
Coat the steaks with the pepper, pressing it gently into the meat. Heat a large, heavy sauté pan over high heat until very hot but not smoking. Add the oil and swirl to coat the bottom of the pan. Add the steaks and cook without disturbing for 4 to 5 minutes, or until they release from the pan and are crusty and brown. Using tongs, turn the steaks and continue to cook over high heat another 2 to 3 minutes, or until the desired doneness. Moisture will just begin to accumulate on the surface of the steaks when they are medium-rare. Remove the steaks to a plate and tent with foil to keep warm.
Reduce the heat to medium, add the shallot to the pan, and sauté for 30 seconds, or until translucent and fragrant. Add the wine and simmer for a minute or so, scraping up the brown bits from the bottom of the pan with a heat-proof spatula. Add the broth and thyme and simmer another 5 to 6 minutes, or until thickened and saucy. Remove the pan from the heat, discard the thyme, and let cool for a minute or two. Whisk in the butter quickly, stir in any accumulated juices from the steaks, and season to taste with salt.
Arrange the steaks on individual plates, divide the sauce among them, and serve immediately.
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