Put anchovies (if using), garlic, egg yolk, dijon mustard, lemon juice, and water in a blender and process for about 30-40 seconds, until the mixture is smooth.
With the blender running, pour the extra virgin olive oil in slowly, until you reach the desired consistency.
Remove dressing to bowl. Stir in the parmesan cheese and ground pepper.
Put chopped kale, pomegranate arils, and avocado, and croutons in a large bowl,
Slowly pour dressing into bowl (you may not need it all) and toss ingredients together.