Heat oil in a large skillet over medium. Add chicken, garlic, onions, salt and pepper and cook, stirring occasionally, until chicken is cooked through. Add the carrots, cabbage, and green onions, cooking for a few more minutes until vegetables are tender, but still have a nice crunch.
In a small bowl combine the sweet chili sauce, ginger, chunky peanut butter, and soy sauce, and crushed red pepper. Stir until smooth. Add to pan, along with chopped cilantro. Stir until blended in and heated through. Spoon mixture into lettuce leaves.
Layer tortillas with a handful of lettuce, peanuts, snap peas, and a large spoonful of the chicken mixture. Roll tightly like a burrito and secure with a toothpick.