To make the croutons, first preheat the oven to 400 degrees F (200 degrees C).
In a bowl, toss the Brioche (3 slice) with the Olive Oil (2 tablespoon) and a pinch of Kosher Salt (to taste). Add Herbes de Provence (1/2 teaspoon), if using.
Spread the bread evenly on a baking sheet and bake until golden brown and crisp, about 15 minutes. Midway through baking, redistribute the croutons if they are coloring unevenly.
To make the dressing, mince the Garlic (3 clove) and Anchovy Fillets (6) together on a cutting board.
Add a pinch of Kosher Salt (to taste) and mince further. Every so often, using the side of your knife, drag the mixture against the cutting board to create a paste. Transfer to a bowl.
Whisk the yolk of the Large Egg (1) and the White Balsamic Vinegar (1/4 cup) into the bowl.
Slowly drizzle in Olive Oil (1 cup), whisking constantly until a thick dressing forms. Taste the dressing and add more salt or vinegar to taste.
Add water, a small spoonful at a time, stirring to thin dressing to the consistency of heavy cream.
In a large bowl, combine the Kale (2 pound) and the croutons. Pour the dressing to taste (I didn't use all of it) over top and toss to coat.
Add the Parmigiano-Reggiano (2/3 cup) and toss again, then serve.