Adjust oven rack to middle position and heat oven to 400 degrees. Cut steak in half lengthwise with grain, then cut each piece in half crosswise against the grain to make 4 equal size steaks. Pat dry with paper towels and season with salt and pepper.
Heat oil in 12" skillet over medium-high heat until just smoking. Add 1 T butter and swirl to melt. Lay steaks in pan and cook until well browned, 3-5 minutes per side. Move skillet to oven and cook until steaks register 125 degrees (for medium rare), 3-5 minutes. Transfer steaks to place and tent loosely with foil.
Return skillet with drippings to medium-high heat (skillet handle will be hot). Add 1 Tbs. butter and shallot and cook until shallot is browned, about 2 minutes. Add wine and any accumulated beef juices from plate and bring to a boil, scraping up any browned bits. Continue to boil until slightly thickened and reduced to about 1/2 c, about 5 minutes.
Remove sauce from heat and swirl in remaining butter until melted. Season with salt and pepper to taste. Slice steaks thin against grain on bias and serve with sauce.