Step 1

Freeze the beef for 20 minutes; transfer to a clean work surface. Slice diagonally (across the grain) into 1/8-inch-thick strips. In a small bowl, whisk together the soy sauce, sesame oil, brown sugar, garlic, and ginger. Place the onions and peppers in a small bowl; toss with half the soy marinade. Toss the steak in the remaining marinade; let stand for 15 minutes.

Step 2

Heat 2 teaspoons of the vegetable oil in a large nonstick skillet over medium-high heat. Add the onions and peppers; cook until softened, about 5 minutes. Transfer to a plate. Wipe the skillet clean with a paper towel.

Step 3

Heat the remaining 2 teaspoons vegetable oil over high heat. Cook half the meat, turning often, until browned, about 2 minutes. Transfer to a plate. Cook the remaining meat. Return the first batch and any accumulated juices to the pan; add the onion mixture. Cook, tossing, until heated through, about 1 minute. To serve, roll up the beef mixture in lettuce leaves.