Croissant Steak Sandwiches with Caramelized Onions and Horseradish Mayonnaise

Preparation Mix mayonnaise and horseradish in small bowl to blend. Melt 1 tablespoon butter in heavy large skillet over medium-high heat. Sprinkle tenderloin steaks with salt and pepper. Add steaks to skillet and cook to desired doneness, about 5 minutes per side for medium-rare. Using tongs, transfer steaks to work surface. Melt 3 tablespoons butter in same skillet over medium-high heat. Add onions; sauté until dark brown, about 25 minutes. Add mushrooms; sauté until tender, about 5 minutes. Add broth; boil until juices are reduced to glaze, stirring occasionally, about 1 minute. Season onion mixture to taste with salt and pepper. Place 1 croissant bottom, cut side up, on each of 4 plates. Spread each with horseradish mayonnaise and top with 1/2 cup arugula. Thinly slice steaks and divide among croissants. Top with onion mixture. Spread remaining mayonnaise on cut side of croissant tops. Place tops on sandwiches.

Preparation Mix mayonnaise and horseradish in small bowl to blend. Melt 1 tablespoon butter in heavy large skillet over medium-high heat. Sprinkle tenderloin steaks with salt and pepper. Add steaks to skillet and cook to desired doneness, about 5 minutes per side for medium-rare. Using tongs, transfer steaks to work surface. Melt 3 tablespoons butter in same skillet over medium-high heat. Add onions; sauté until dark brown, about 25 minutes. Add mushrooms; sauté until tender, about 5 minutes. Add broth; boil until juices are reduced to glaze, stirring occasionally, about 1 minute. Season onion mixture to taste with salt and pepper. Place 1 croissant bottom, cut side up, on each of 4 plates. Spread each with horseradish mayonnaise and top with 1/2 cup arugula. Thinly slice steaks and divide among croissants. Top with onion mixture. Spread remaining mayonnaise on cut side of croissant tops. Place tops on sandwiches.