Season the filet well on all sides with salt and pepper. Heat a small skillet over medium-high heat until hot. Add the olive oil and the filet to pan and cook for 2 minutes on all sides for medium-rare, 6 to 8 minutes total. Remove from the pan to a cutting and tent with foil to keep warm. Let rest for 5 minutes.

Make the bernaise sauce: In a saucepan combine shallots, lemon juice,vinegar and tarragon stems and cook over medium heat until liquid has reduced to 2 tablespoons. Let reduction cool to room temperature.

In a metal bowl, combine egg yolk, water and reduction over a pot of simmering water. Whisk well until egg mixture begins to form ribbons when whisk is lifted out of mixture. While continuing to whisk, drizzle in melted butter little by little until completely incorporated and sauce is thick. Add chopped tarragon, taste and season with salt and white pepper.

To make the sandwiches, thinly slice the tenderloin and divide it equally between the bottom halves of the ciabatta rolls. Divide the arugula,  the tomatoes and the onions and place on top  of the beef. Drizzle the bernaise sauce over the top and place the top half of the roll on each sandwich. Serve with the remaining bernaise sauce.