Cut each spring onion in half lengthwise, then cut each length in half into 2 pieces, about 4 inches long. Set aside.
Trim ends of asparagus spears so that just 4 inches of the floret end remains. Set aside.
Lay out beef slices on a work surface, like tall rectangles. Place a green and a white portion of onion and 1 piece of asparagus across the bottom of the beef rectangles. Roll each portion tightly into a cylinder; secure each portion with 1 or 2 toothpicks.
Brush each roll with teriyaki sauce.
Preheat the grill, grill pan or broiler. Grill or broil for 3 minutes. Turn over and baste each portion again with teriyaki sauce. Cook for another 3 minutes.