Preheat oven to 400°. Place asparagus, tomatoes and walnuts in a greased 15x10x1-in. baking pan. Mix oil, oregano, salt and pepper; add to asparagus mixture and toss to coat.
Roast until asparagus is crisp-tender, 15-20 minutes, turning vegetables occasionally. Sprinkle with cheese. Top with basil before serving.