Mix soy sauce, mirin, and sake in small bowl to blend; set stir-fry sauce aside.
Place chicken slices in medium bowl; sprinkle with salt and pepper.
Add cornstarch and toss to coat.
Heat 2 tablespoons oriental sesame oil in large deep nonstick skillet over high heat.
Add chicken slices and sauté until cooked through, about 4 minutes.
Using slotted spoon, transfer chicken slices to bowl. Add stir-fry sauce and toss to coat. Season stir-fry mixture to taste with salt and pepper. Transfer mixture to strainer set over bowl to drain.
Arrange lettuce leaves on serving platter. I like to double them up so they are sturdier.
Divide stir-fry mixture among leaves. Add veggies to each wrap, then drizzle peanut sauce and crushed peanuts on top.