Cut chicken into bite-size pieces and marinate in lime juice for at least 2 hours in the fridge. Make a dressing by chopping garlic, ginger & peppercorns. Blend in basil, soy sauce, vinegar, honey, water and grated lemon peel. Pour that mixture into blender and process with 2 tb olive oil.
Saute chicken in sesame oil & 3 tb olive oil. Add dressing & stir. Mix in peanut butter and mushrooms. Add cornstarch mixture and stir. Sprinkle green onions on top and serve over rice.