Wash romaine under cold running water. Trim core, and separate stalk into leaves; discard wilted or discolored portions. Shake leaves to remove moisture. Place romaine in a large zip-top plastic bag; chill at least 2 hours.
Combine olive oil and next 5 ingredients in a jar. Cover tightly, and shake vigorously. Set aside.
Cut coarse ribs from large leaves of romaine; tear leaves into bite-size pieces, and place in a large salad bowl. Pour dressing over romaine; toss gently until coated.
Squeeze juice from lemon halves over salad. Grind a generous amount of pepper over salad; sprinkle with cheese. Toss salad. Top with Garlic Croutons and, if desired, anchovies. Serve salad immediately.