The fillet should have been at room temperature for approx. 30 minutes before grilling. Season with salt and pepper just before grilling. Brown the fillet quickly on all sides. Place the fillet on the upper grill in the grill and let it enjoy itself there. If you use a roasting thermometer, 60 degrees is a nice temperature.
Peel the onion and bake in a refractory form with 1 tablespoon oil and 1 tablespoon butter for 2 hours at 150 degrees.