In a large saucepan, bring 3 cups water to a boil. Add asparagus; cover and boil for 3 minutes. Drain and immediately place asparagus in ice water. Drain and pat dry. Transfer to a serving bowl. Stir in the tomatoes.
In a small bowl, whisk the vinegar, basil, oil, salt and pepper. Drizzle over vegetables; toss to coat. Cover and refrigerate for at least 1 hour. Just before serving, stir in cheese. Yield: 6 servings.