Tightly wrap beef tenderloin in kitchen film or parchment and place in freezer for about 2 hours. If using parchment, place inside a glass container with lid.
Using hand blender and a small bowl—or shaking combined ingredients in a Mason jar—mix olive oil, vinegar, mustard, pomegranate molasses, honey, pepper, and 1/4 tsp salt. Set aside.
When ready to serve, place serving plate in freezer to keep cold. Place a second plate in freezer to hold the pieces of tenderloin as you work.
Remove tenderloin from freezer and cut into 5 to 6 slices. Place one slice in between two pieces of parchment and beat with flat wooden mallet or rolling pin until paper thin. Keep the other slices wrapped on the plate in freezer. Place beaten piece of carpaccio onto serving plate in freezer and remove each slice of beef to repeat the process until each piece has been beaten into carpaccio and returned to freezer.
In small bowl, combine arugula with 1 Tbsp pomegranate arils and spoonful of prepared dressing. Remove carpaccio from freezer, season with remaining salt, and drizzle with remaining dressing. Arrange arugula in centre of serving plate over carpaccio and sprinkle remaining pomegranate arils over top.