Pat the steaks dry with paper towels. Season both sides generously with salt and pepper.
Heat a medium skillet over high heat until very hot. Add the olive oil, then place the steaks in the pan.
Sear until nicely browned, about 1–3 minutes per side. Continue cooking, flipping every minute, until the internal temperature reaches at least 110°F for medium-rare (or your desired doneness).
Remove the steak from the skillet and let it rest while you prepare the gravy.
Make the gravy: In the same skillet over medium-high heat, add the butter, minced shallots, and sliced mushrooms. Cook, stirring occasionally, until the mushrooms release their liquid and the shallots are browned (about 5 minutes).
Add the red wine and boil, stirring often, until the liquid is reduced and syrupy (about 3 minutes).
Add the beef broth and continue cooking until the sauce is reduced and thickened. Season with salt and pepper to taste.
Slice the rested steak against the grain and serve with the red wine & mushroom gravy spooned generously over the top.