Take the beef tenderloins and drizzle with olive oil. Season well all over with plenty of kosher salt and freshly ground black pepper all over. Make sure they are at room temperature before cooking.
Place a cast iron skillet over medium-high heat on the stove top, add a small amount of oil to the pan. When oil shimmers, place tenderloins in pan. When juices begin to rise to the surface of the meat, about 2-3 minutes, flip steaks with tongs and sear the other side for another couple minutes and check doneness with an instant-read thermometer.
Thermometer when inserted into the thickest part (from the side) of the meat should read 135 degrees F for medium-rare.
Remove from pan and tent with foil while you let it rest for 5 minutes before cutting into.
Make the bearnaise reduction first. In a small saucepan, combine half of the tarragon, shallots, vinegar and wine over medium-high heat. Bring to a simmer and cook until reduced by half. Remove from heat and set aside to cool. Blend yolks and bearnaise reduction together in a blender. With the blender running, add ⅓ of the butter in a slow steady stream. Once it emulsifies, turn the blender speed up to high and add the remaining butter. Add the remaining half bunch of fresh tarragon leaves, season with salt and pepper and give it 1 more buzz. Set aside in a warm spot to hold the sauce.
Recipe by Wishes and Dishes at https://wishesndishes.com/filet-mignon-with-blender-bearnaise-sauce/