Pat the steak dry and season both sides with salt and pepper to taste.
Place the oil in a large pan over high heat. Arrange the steaks in a single layer in the pan; if they don't all fit you might need to work in batches.
Cook the steak for 3-4 minutes per side or until desired level of doneness is reached. You can use a thermometer if needed to gauge the proper temperature of the meat.
Remove the steak from the pan. Place on a plate and cover to keep warm.
Reduce the heat to medium and melt the butter in the pan. Add the mushrooms and cook for 4-5 minutes, stirring occasionally, until the mushrooms are browned and tender.
Add the shallots and garlic and cook for one more minute. Season the vegetables with salt and pepper to taste.
Pour the cognac into the pan and bring to a boil. Cook for 1-2 minutes or until liquid has reduced in half.
Add the beef broth, Dijon mustard, worcestershire sauce and heavy cream to the pan. Whisk until well combined.
Bring the sauce to a simmer. Cook for 3-4 minutes or until sauce has just thickened.
Return the steaks to the pan. Spoon the sauce over the meat. Sprinkle with chives, then serve.