Cut chicken into bite-size pieces and marinate in lime juice for at least 2 hours in refrigerator. Make a dressing by chopping garlic, ginger, and peppercorns in food processor or blender ultil pepper is no longer whole. (It will probably be impossible to break up all peppercorns.) Blend in basil, soy sauce, vinegar, honey, water, and grated lemon peel. Pour 2 tablespoons of the olive oil into the processor or blender and process until smooth. Set dressing aside. Remove chicken from marinade and saute it in sesame oil and the remaining 3 tablespoons of olive oil until it turns white. Add dressing and stir until chicken is well coated and sauce is warm. Mix in peanut butter. Stri in mushrooms, Add cornstarch mixture to thicken sauce. Sprinkle green onions on top and serve over rice.