In a large, non-reactive bowl, combine 1/2 cup soy sauce, the minced garlic, 1 tablespoon of the sesame oil, 1 teaspoon of the mirin, and the red pepper flakes. Add the meat toss to coat. Cover and refrigerate overnight, turning occasionally.

Preheat the grill. Mix the remaining 1/4 cup soy sauce with remaining 1 teaspoon of sesame oil. Add the green onions (scallions), and garlic, and toss to combine. Set aside. In a small bowl, combine the remaining teaspoon of mirin, the chili powder and sesame seeds.

Remove the steak from the marinade and pat dry. Grill for 1 minute on each side for medium-rare.

Lay the lettuce leaves on a flat work surface and rub the mirin mixture on the insides of the leaves. Set aside.

Lay several slices of cooked steak in center of each leaf, drizzle with about 1 tablespoon of the seasoned green onions (scallions), and top with 2 garlic slivers. Fold the lettuce over the steak and wrap tightly. Repeat with the remaining ingredients and serve immediately.