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.
Heat a large nonstick skillet or griddle over medium heat. Using a serrated knife, slice the croissants in half lengthwise. In 2 batches, place the croissant halves, cut side down in the skillet and cook for 30 seconds to 1 minute until lightly toasted. Lay the Brie slices over the toasted croissant halves. Place about 1/4 cup 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.