How to Make It
In a small skillet, toast the sesame seeds over moderate heat until lightly browned, about 3 minutes. Let cool.
In a large glass baking dish, combine 3 tablespoons of the sake with the soy sauce, ginger, garlic, minced scallions, 2 teaspoons of the sesame seeds, 1 1/2 teaspoons each of the canola oil and sugar and a pinch of cayenne pepper. Add the meat and turn to coat. Let marinate at room temperature for 20 minutes.
Heat a large, heavy skillet. Add 2 tablespoons of the canola oil and swirl to coat. Add about one-fourth of the meat at a time in a single layer and cook over high heat until browned and crisp around the edges, about 2 minutes per side; transfer to a large platter. Repeat with the remaining meat, adding more oil as needed.
In a medium bowl, combine the remaining 2 teaspoons of sake with the sesame oil, a pinch of cayenne, the remaining 1 teaspoon of toasted sesame seeds and 1 teaspoon of sugar. Add the scallion matchsticks.
Arrange the lettuce leaves on the platter alongside the grilled meat and serve with the scallion salad and the chili paste on the side.