In a saucepan, cook the asparagus in a small amount of water for 5 minutes or until crisp-tender. Rinse with cold water; drain well.
Place in a bowl; add pimientos and onions. In a small bowl, whisk oil, vinegar, mustard, Worcestershire sauce, basil, salt, pepper and thyme; pour over asparagus mixture and toss to coat. Cover and refrigerate for at least 2 hours.