1. For marinade, in a screw-top jar combine oil. vinegar, basil, thyme and marjoram. Add sugar, if desired. Cover and shake well. Set aside 1/4 cup in refrigerator for dressing.
2. Place meat in a resealable plastic bag set in a shallow dish. Pour marinade over meat; seal bag. Marinate in refrigerator 4 to 6 hours, turning bag occasionally.
3. Meanwhile, remove stems from bell peppers. Halve lengthwise; remove seeds and membranes. Cut peppers into 1-inch-wide pieces.
4. Preheat grill to medium. Drain meat, reserving marinade. Grill meat, uncovered, to desired doneness, turning onc. Allow 14 to 18 minutes for medium rare (145°) and 18 to 22 minutes for medium (160°). Add pepper strips the last 8 to 10 minutes of grilling, turning and brushing with marinade occasionally during the first 5 minutes of cooking. Discard any remaining marinade.
5. Thinly slice meat. To serve, arrange basil leaves and pepper strips on rolls; top with steak slices. Drizzle each sandwich with dressing.