In a small mixing bowl, combine the lemon juice, olive oil, Dijon, capers and a pinch of salt and pepper.
Thinly slice about 6 pieces of filet mignon. Lay out a piece of plastic wrap about 1 foot long, add a piece of the beef, and place another piece of plastic on top of the beef. With a meat mallet or something heavy, gently pound and expand the circumference of the beef. Transfer to a plate, and repeat the process with the remaining pieces.
On top of the layer of flattened beef, drizzle some of the olive oil mixture. Sprinkle with flaky sea salt. Add radish slices and tomatoes; sprinkle salt on each tomato. Add some tarragon and shallots. Top with more dressing, then add shaved cheese. Add another sprinkle of salt and pepper, and drizzle with remaining dressing.