1Heat gas or charcoal grill. In small bowl, mix ginger, salt and pepper. Brush pork with oil; rub and press ginger mixture on all sides of pork.
2Place pork on grill over medium heat. Cover grill; cook 17 to 20 minutes, turning several times, until meat thermometer inserted in center reads 145°F. Remove from grill. Cover; let stand 3 minutes before slicing.
3Meanwhile, in small bowl, mix aioli ingredients. Cut pork into thin slices; serve with aioli.