Season the steaks with salt and pepper. In a medium skillet, melt the butter over medium-high heat. Cook the steaks for about 5 minutes each side for medium-rare. Set aside for 5 minutes before slicing. Slice the steak, across the grain, into 1/4 to 1/2-inch thick slices.

Using a serrated knife, slice the croissants in half lengthwise. Lay the Brie slices over the bottom croissant halves. Place about a small amount of the arugula on the bottom halves of the croissants. Add the sliced steak. Arrange the red bell pepper on top of the steak. Top with the remaining arugula and add the top of the croissant. Serve immediately.