1/2 cup mayonnaise
1/4 cup prepared white horseradish
4 tablespoons (1/2 stick) butter, divided
3 1-inch-thick beef tenderloin steaks
3 medium onions, thinly sliced
8 ounces large shiitake mushrooms, stemmed, caps thinly sliced (about 5 cups)
1 cup beef broth
4 large croissants, halved horizontally, lightly toasted
2 cups arugula
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.
Makes 4 servings.