Trim all visible fat and butterfly the beef eye round roast by cutting horizontally through the center (parallel to the surface of the meat) the length and width of the roast. Do not cut through the opposite side. The meat should lay flat.
Combine wine, vinegar, garlic, mustard, pepper and sugar. Place beef roast in utility dish or plastic bag, add marinade, turning to coat. Cover dish or tie bag and marinate in refrigerator 6 to 8 hours or overnight.
Remove roast from marinade; reserve marinade. Place roast on broiler pan
and broil for 20 minutes, turning and basting with reserved marinade
occasionally