Place the beef tenderloin in the freezer and chill for 1 hour.

Using a very sharp knife, cut the beef across into 1/8-inch-thick slices.

Place the beef between two sheets of cling wrap film and pound lightly until thin enough, almost paper thin. Arrange the beef slices into the serving plates.

In a small bowl, whisk together the lemon juice, the mustard and the sugar. Gradually whisk in the olive oil to make an emulsion. Season with salt and pepper.

Pour half of the dressing over the beef.

Place a pile of arugula over the beef. Arrange the mushroom slices around it. Drizzle the arugula and the mushrooms with some of the dressing. Arrange the shaved parmesan cheese on top. Decorate the places with lemon slices and serve immediately.