Wash lettuce under cold running water. Trim core, and separate stalk into leaves; discard wilted or discolored portions. Shake leaves to remove moisture. Place lettuce in large zip-top plastic bag; chill at least 2 hours.
Combine olive oil and next five ingredients in a jar. Cover tightly, and shake vigorously. Set aside.
Cut coarse ribs from large leaves of lettuce and discard. Tear leaves into pieces, and place in a large salad bowl. Pour dressing over lettuce; toss gently.
Squeeze juice from lemon halves over salad; shave cheese over salad. Top with Garlic Crostini and anchovies. Serve immediately.