Combine lemon juice, anchovies, garlic, and mustard in a blender or food processor fitted with a steel blade. Process until thoroughly combined. Pour in olive oil very gradually through the feed tube while machine is running, first 1 tablespoon at a time, then gradually increasing the amount. Season with salt and pepper.

Stack and bunch the kale leaves together on a cutting board and cut across the stack into skinny slivers.

Place the kale, croutons, and Parmesan cheese in the bowl and drizzle with about a 1/4 of the dressing. Toss and taste the salad and add more dressing if desired, then toss again.