Snap off tough ends of asparagus; arrange asparagus and dried tomatoes in a steamer basket over boiling water. Cover and steam 2 to 4 minutes or until asparagus is crisp-tender. Set tomatoes aside. Plunge asparagus into ice water to stop the cooking process; drain. Cut asparagus into 1-inch pieces, and chill until ready to use. Chop tomatoes.
Whisk together garlic and next 8 ingredients in a medium bowl; add asparagus, tomatoes, beans, onion, and capers, tossing to coat. Cover and chill 1 hour. Serve asparagus mixture over salad greens; sprinkle with cheese.