Whisk together soy sauce, and brown sugar in a small bowl until sugar is dissolved. Set aside. Cut beef crosswise into 1/4-inch-thick slices. Flatten each piece of beef, with a meat pounder, until it is 1/8-inch-thick. Don't over flatten. Transfer slices to a large plate.
Dip a slice of beef into soy mixture and place on a clean surface. Season with pepper. Put 2 pieces of scallion green and 1 piece of each pepper across the width of beef. The vegetables should extend over both edges. Roll up lengthwise and skewer near the edges with 2 toothpicks. Set aside. Repeat with remaining beef and vegetables.
Brush a grill pan with oil and heat until hot, or heat oven broiler. Grill or broil the rolls, brushing with the sauce and turning until the meat is medium rare, 2 to 4 minutes. Cut each roll in half. In a small saucepan bring remaining sauce to a boil for 3 to 5 minutes. Pour into a small bowl, add scallion rings, serve on the side.