Red Wine–Mushroom Pan Sauce

Prepare all ingredients for the pan sauce while the steaks are in the oven.

After transferring steaks to wire rack, pour off fat from now-empty skillet. Heat oil over medium-high heat until just smoking. Add mushrooms and cook, stirring occasionally, until beginning to brown and liquid has evaporated, about 5 minutes. Add shallot and cook, stirring frequently, until beginning to soften, about 1 minute. Increase heat to high; add red wine and broth, scraping bottom of skillet with wooden spoon to loosen any browned bits. Simmer rapidly until liquid and mushrooms are reduced to 1 cup, about 6 minutes. Add vinegar, mustard, and any juices from resting steaks; cook until thickened, about 1 minute. Off heat, whisk in butter and thyme; season with salt and pepper to taste. Spoon sauce over steaks and serve.