Place turkey in a plastic bag set in a shallow dish.
In a small bowl, whisk together peanut oil, lime juice, garlic, and sesame oil. Pour over turkey in plastic bag. Close bag. Marinate in the refrigerator for 4 hours, turning bag occasionally.
For sauce, drain marinade into food processor bowl or blender container. Add chicken broth, peanut butter, jalapeno pepper, soy sauce, gingerroot, and sugar. Cover and process or blend until smooth. Transfer to a small saucepan. Bring mixture to boiling over medium heat.
In a covered grill, arrange preheated coals around a drip pan for indirect grilling. Test for medium heat above the pan. Place turkey tenderloins on grill rack over drip pan.
Cover and grill for 25 to 30 minutes or until tender and no longer pink (170 degrees F), turning once and brushing with sauce during the last 5 to 10 minutes of grilling. Let stand for about 5 minutes.
Slice turkey across the grain; arrange slices on a platter. Pour some of the remaining warm sauce over turkey and pass any remaining sauce. Garnish with the snipped cilantro. Makes 6 to 8 servings.
When working with chili peppers, wear plastic or rubber gloves because chili peppers contain volatile oils that can burn your skin and eyes. If your bare hands touch the chili peppers, wash your hands well with soap and water.