Sprinkle steaks with salt and pepper. Warm oil in a large skillet over medium-high heat. Add steaks and cook, turning once, about 4 minutes total for medium-rare. Transfer to a plate, and cover loosely with foil to keep warm.
Wipe skillet with a paper towel and add broth. Bring to a boil and cook until reduced by half, about 5 minutes. Remove pan from heat and whisk in mustard and butter. Season with salt and pepper, spoon over steaks, and serve.