In a small bowl, combine vinegar, oil, basil, mustard, garlic and sugar to make marinade. Place steak and 1/3-cup of the marinade in a sealable plastic bag. Close bag securely, turn to coat steak and marinate in refrigerator 15 minutes to 2 hours, turning occasionally. Cover and refrigerate remaining marinade.
Meanwhile, bring 1-inch of water to a boil in a large skillet. Add the asparagus and reduce heat to medium-low. Cover and cook 2-3 minutes or until asparagus is just crisp-tender. Drain asparagus and combine with the reserved marinade tossing to coat.
Remove the steak from the marinade and discard used marinade. Grill over medium heat or medium coals. Grill uncovered for 16-20 minutes for medium rare (145° F) to medium (160° F) doneness, turning once.
Season steak and asparagus with the salt and pepper. Carve steak crosswise into slices and serve with the asparagus.