1In small bowl, mix all Wasabi Aioli ingredients. Cover and refrigerate until serving.
2If tuna steaks are large, cut into 8 serving pieces. In shallow glass or plastic dish or resealable food-storage plastic bag, mix vegetable oil, soy sauce, brown sugar, sesame oil, gingerroot and garlic. Add tuna; turn to coat with marinade. Cover dish or seal bag and refrigerate, turning once, at least 2 hours but no longer than 4 hours.
3Heat coals or gas grill for direct heat. Remove tuna from marinade; reserve marinade. Cover and grill tuna about 4 inches from medium heat 10 to 15 minutes, brushing 2 to 3 times with marinade and turning once, until tuna flakes easily with fork. Discard any remaining marinade. Sprinkle tuna with sesame seed. Serve with Wasabi Aioli.