Place the steak in the freezer for 30 minutes to firm up slightly, then slice thinly against the grain, using a sharp knife. Lightly freezing the meat will help you slice it more easily.
Place the sliced steak in a large bowl and add all the bulgogi ingredients except the vegetable oil. Mix together thoroughly, then cover and refrigerate for 3 to 4 hours.
In a large skillet, heat the vegetable oil over medium-high heat. Scoop out the steak, using a slotted spoon to allow any excess sauce to drip off, then fry the steak in hot oil. Use tongs to separate the steak slices during cooking, and cook until cooked through, about 5 minutes. Remove the steak from the heat.
ASSEMBLE THE WRAPS:
Place the lettuce, underside-up, on a large platter and fill with the bulgogi beef, carrot, cucumber, bell pepper and scallions. Sprinkle with sesame seeds before serving.