Preheat oven to 375° Fahrenheit. Place roughly chopped kale leaves in large bowl and set aside.
Place torn bread pieces on baking sheet and drizzle olive oil over, then sprinkle salt and pepper over. Use hands to toss and coat bread pieces fully in oil, then spread bread out across baking sheet in one even layer.
Place baking sheet in preheated oven. Bake 10 minutes, tossing bread occasionally to brown evenly. After 10 minutes, transfer croutons to medium bowl and set aside. Note: for crispier croutons, bake croutons up to 15 minutes total, tossing croutons occasionally. When desired doneness is achieved, transfer croutons to bowl and set aside.
With sharp kitchen knife, roughly chop anchovies and garlic clove, then transfer ingredients to food processor bowl. Add egg yolks, lemon juice, and dijon mustard.
Secure lid on food processor and process ingredients until anchovies and garlic are finely chopped. Keep food processor running and slowly drizzle neutral oil into food processor bowl, drop by drop. Mixture should become thick after approximately 50% of oil has been added.
Once mixture thickens, continue adding oil slowly, now in 1-tablespoon increments rather than drop by drop.
When all oil is incorporated, add grated parmesan to food processor. Pulse 1 to 2 times or until parmesan and dressing mixture are just combined.
Pour desired amount of salad dressing over kale leaves in large bowl. Use hands to gently massage dressing into kale, making sure to coat as many pieces as possible. When satisfied, top salad with croutons and parmesan shavings, then serve immediately.