For dressing, combine anchovies, garlic, salt, pepper, vinegars, tomatoes and parsley in food processor. bowl and process until smooth. With machine running, add oil in a steady stream until thoroughly combined.
Remove dressing from food processor and set aside. (May be made ahead and refrigerated for several days. Allow to come to room temperature before using.) In a large bowl, toss together remaining ingredients; toss with dressing and portion onto salad plates.