Place beef in large resealable plastic food storage bag. Combine soy sauce, water, honey, oil, ginger, allspice, red pepper, and garlic in small bowl. Pour over meat in bag. Seal bag; turn to coat meat. Marinate in refrigerator for 4 to 16 hours, turning bag occasionally.
Meanwhile, place 1-inch of water in medium saucepan. Bring water to a boil. Add carrots. Cover; cook 5 minutes or until crisp-tender. Drain.
Prepare grill for direct cooking. Drain meat. Discard marinade. Alternately thread meat and carrot pieces onto 4 soaked wooden skewers. Add green onion piece to end of each skewer.
Grill kabobs over medium coals 11 to 14 minutes or until meat is tender, turning once during grilling.