Slice beef with the grain into long strips, about 1 1/2 inches wide, and place into a bowl. Stir together the soy sauce, rice wine, sugar, garlic, sesame oil, pepper, and chile paste in a small bowl. Pour one third of this mixture over the beef, and toss to coat. Marinate at least one hour at room temperature, or longer in the refrigerator. Simmer the remaining sauce, and the green onions in a small saucepan for one minute before pouring into a serving dish to cool.
Wash and dry the lettuce, and trim off any large stems. Gently flatten the leaves with the side of a cleaver or large knife. Arrange on a serving dish.
Preheat a grill for medium-high heat and lightly oil grate.
Place grate three inches over the coals. Cook the meat to desired doneness, about three minutes per side for medium rare. Slice against the grain into thin strips.
To serve, each diner places some beef and sauce into a lettuce leaf, folds it into a bundle, and eats it with their fingers.