Season steaks on both sides with 1/4 teaspoon pepper and salt. Heat oil in a large skillet over medium-high heat. Reduce heat to medium, add the steaks and cook 3 to 5 minutes per side for medium. Transfer to a plate and tent with foil to keep warm.

Add mushrooms to the pan and cook, stirring, until golden brown and beginning to release their juices, about 3 minutes. Add brandy and cook, stirring, until almost evaporated, about 1 minute. Add broth, bring to a boil and cook until reduced by half, 8 to 10 minutes.

Meanwhile, combine butter and flour in a small bowl to form a paste. When the pan sauce is reduced by half, whisk in mustard, then gradually whisk in the butter-flour paste a few bits at a time and cook until the sauce thickens, about 1 minute. Reduce heat to medium-low. Return the steak to the pan along with any accumulated juices. Turn to coat with the sauce and cook until heated through, about 1 minute. Top the steak with the sauce and sprinkle with chives.