Cook asparagus and pepper strips in a skillet with just a bit of water, covering to steam for about 4 minutes. Drain. Season with salt and pepper to taste. Set aside.
Tenderize each steak by either piercing all over numerous times on both sides with a fork or by pounding on just one side with a meat mallet or heavy frypan.
Season tenderized side of each steak with salt and pepper. Spread each with mustard and cheese. Add 3 asparagus spears and pepper strips to each steak and sprinkle each with nuts if desired. Roll up like jelly roll and tie each with 2 to 3 pieces of butcher twine. Season each bundle (involtini) all over with salt and pepper.
Pan-sear in well-oiled hot cast iron or nonstick pan until browned all over. Reduce heat to medium and continue to cook, covered, turning each often until cooked to 145ºF (63ºC) for medium-rare when tested with a digital instant read thermometer. Let stand for 5 minutes before serving.