Preheat a grill or broiler; fire should be quite hot.
Place the meat between two layers of wax paper or plastic wrap and pound it gently so that it is about 1/8-inch thick.
Brush one side of each piece of meat with a little soy sauce.
Cut the scallions into length about the same width as the meat and place a small bundle of them at one of the narrow ends of each slice.
Roll the long way, securing the roll with a toothpick or two.
(You can prepare the rolls in advance up to this point; cover and refrigerate for up to 2 hours before proceeding) Brush the exterior of the roll with a little more sauce.
Grill until brown on all sides, a total of about 6 minutes for chicken, 4-5 minutes for pork or veal, 4 minutes or less for beef.
Optional fillers: Scallions work very well; so do chives.
You could also use small amounts of lightly cooked, chopped spinach or chard; cooked, chopped shiitake (or other) mushrooms; julienned and lightly cooked carrots; parboiled asparagus spears.
As alternatives to soy sauce, you can use asian fish sauce (nam pla or nuoc mam), chinese hoisin sauce, or premade teriyaki sauce.