Cut the chicken into strips. Mix the vegetable oil, 1 T soy sauce, honey, garlic and ginger in a medium bowl. Add the chicken and mix until coated. Thread the chicken onto soaked wooden skewers and place on a grill rack. Grill for 10 minutes or until the juices run clear, turning frequently. Bring the broth, 2 T soy sauce, vinegar and sesame oil to a simmer in a small saucepan. Add the peanut butter and stir until well blended. Arrange the chicken on skewers on a platter lined with Boston lettuce leaves, julienned carrots and daikon (Asian radishes). Serve with the hot peanut sauce for dipping.
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