Heat oven to 375°F. Toss bread with 2 tbsp oil, 1/4 tsp salt, and 1/4 tsp pepper on a sheet pan.
Bake croutons until golden and crisp, 9–12 minutes, stirring once. Cool slightly.
Wash, dry, and chop kale. Place in a large bowl.
Whisk mayonnaise, lemon juice, Dijon, anchovy paste, and garlic until smooth.
Stream in 3 tbsp oil while whisking. Stir in Parmesan. Thin with water to desired consistency.
Massage kale with about half the dressing for 30–60 seconds until slightly softened.
Add warm croutons and remaining dressing. Toss to coat. Season with salt and pepper.
Finish with extra Parmesan and lemon zest. Serve right away.