Drizzle two teaspoons olive oil on steaks and spread with your hands to cover steaks with a film of oil. Season both sides of steak with salt and pepper. Coat both sides with thyme leaves, pressing with your hands to make them adhere. Heat the two tablespoons olive oil on high heat in a heavy skillet until very hot but not smoking. Add one tablespoon butter, tilting the pan to coat and immediately add steaks and sear until steaks are beginning to brown and a nice crust forms, about 3-4 minutes.
Turn steaks, reduce heat to medium-high and continue cooking until steaks are medium rare, about another 4 minutes depending on thickness of steaks. Remove steaks to a platter and cover loosely with foil to keep warm. Reduce heat to medium and add shallot to pan, cook stirring until shallot begins to soften, about 2 minutes.
Add wine to pan and continue cooking, scraping bottom of pan to loosen brown bits. When almost all wine has evaporated, add chicken broth, raise heat to high and boil until reduced by half. Swirl in remaining butter. Taste sauce and season with salt and pepper if needed, then pour over steaks. Serve immediately.
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