Step 1Cook the egg in boiling water for 2 minutes. Immediately rinse it with cold water until the egg is cool enough to handle. Set aside.
Step 2To make the dressing, whisk together the garlic, anchovies, salt and lemon juice in a small bowl. Peel the egg and add it to the bowl, whisking the dressing until thick, about 1 minute. Slowly drizzle in the oil, whisking vigorously to thicken. Whisk in the cheese. Taste and adjust the flavor. Set aside.
Step 3Separate the romaine leaves. To assemble the salad, pour half of the dressing in the bottom of an oversized bowl. Add the croutons and toss in the dressing until thoroughly coated. Add the lettuce and remaining dressing. Toss just until coated. Divide the salad among 6 plates. Arrange the sliced chicken over the top. Garnish with additional cheese and freshly ground pepper. Serve immediately.