Snap off and discard fibrous stem ends of asparagus. Rinse asparagus; drain. Bring 1 inch of water to boiling in a medium saucepan. Place asparagus in steamer basket; cover and steam for 4 minutes or until asparagus is crisp-tender. Drain. Gently rinse with cool water.
Combine green cabbage, red cabbage, carrot, parsley, and onion in a large bowl. Toss gently with sesame oil, vinegar, and pepper.
Divide asparagus spears among six salad plates; top with cabbage mixture. Makes 6 side-dish servings.