1. Heat 1 1/2 tablespoons oil in a large skillet over medium. Add 1 anchovy fillet to pan; cook 30 seconds or until anchovy has melted into the oil, stirring frequently. Add bread to pan; cook 3 minutes or until browned and toasted on all sides, stirring occasionally. Place croutons in a bowl. Remove pan from heat (do not wipe out pan).
2. Finely chop remaining anchovy fillet. Add garlic to anchovy on cutting board; sprinkle with 1/4 teaspoon salt. Mash with the side of a knife to form a paste. Combine garlic mixture, 1 1/2 tablespoons oil, buttermilk, juice, mustard, and 1/4 teaspoon pepper in a small bowl, stirring with a whisk.
3. Heat remaining 1 1/2 teaspoons oil in pan over medium. Crack eggs over pan; cook 3 minutes or until whites are set. Remove pan from heat.
4. Cut larger kale leaves in half crosswise (leave smaller leaves whole). Place kale in a large bowl; massage gently with your hands 1 minute or until slightly wilted. Drizzle half of buttermilk mixture over kale; toss. Divide kale mixture evenly among 6 plates; top evenly with croutons, Parmesan, remaining buttermilk mixture, and eggs. Sprinkle eggs evenly with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon pepper.