For the beef fillet slices with fennel-arugula-apricot salad, slice the fennel finely, season with salt, pepper and a little lime juice. Pit and quarter the apricots and mix into the fennel, let marinate for about 10 minutes.
Season the steaks on both sides with salt and pepper, sear in a hot pan and let rest briefly. Mix fennel and arugula and season again with olive oil and lime juice.
Arrange the slices of beef fillet on a plate with the fennel and arugula salad, sprinkle with a little coarse pepper and serve immediately.