Carefully separate the head of lettuce, so you have lettuce cups.
In the skillet over medium-high heat, heat the olive oil. Add the garlic and cook for 2 minutes. Add the chicken and cook, breaking up the meat with a wooden spoon, until cooked through, about 5 minutes. Add the soy sauce, and season with salt and pepper. Add the basil leaves and cook for another 30 seconds, until they are just fragrant.
Spoon the chicken mixture into the lettuce cups, top with the cilantro, carrots, and peanuts, if using, and serve.