Wash asparagus. Snap off and discard woody bases. In a medium saucepan bring 1 inch of water to boiling. Place asparagus in steamer basket. Cover; steam asparagus over the boiling water for 4 to 6 minutes or until crisp-tender. Drain. Gently rinse with cool water.
In a large bowl combine cabbage, radicchio, carrot, mint, parsley, and onion. Divide asparagus spears among 8 salad plates; top with cabbage mixture.
In a screw-top jar combine oil, vinegar, lemon peel, lemon juice, garlic, sugar (if using), and pepper; cover and shake to combine. Pour over cabbage mixture. Top with cheese. Makes 8 to 10 side-dish servings.