Toss sliced steak with ½ cup of Momofuku Sweet & Savory Korean BBQ Sauce in a bowl. Cover and let marinate for at least 30 minutes and up to overnight.
Heat a nonstick pan or wok over high heat until hot. Add marinated steak and cook in a single layer for 3 minutes. (If you crowd the steak, it will trap the steam and release too much water, causing the steak to boil rather than sear.) Toss steak and cook for another 1–2 minutes until fully cooked and slightly charred. Remove from heat.
Meanwhile, boil noodles for 3 minutes then drain and quickly rinse in cold water until completely cooled. Toss with sauce packet.
To serve, make lettuce wraps using the lettuce, the chilled noodles, and the steak. Top with sliced cucumbers, carrots, or scallions, if desired.