Start by making the croutons. Heat the oven to 175 degrees. Cut off the edges of the bread and cut it into small cubes. Put the cubes in a long pan and mix with 1 tbsp oil and salt. Toast until the bread turns golden brown. Stir occasionally. Remove from the oven and leave to cool.
Tear the kale leaves from the coarse stalks. Tear the leaves into coarse pieces and massage in about 1 tbsp olive oil. Season the chicken fillets with salt and pepper. Fry in oil and butter in a frying pan on both sides until golden brown. Place in a baking dish and continue cooking in the oven until cooked through with an internal temperature of 72°.
While the chicken is in the oven, whisk together the egg yolk, garlic, anchovies, lemon, and Worcestershire sauce. Add the oil in a thin stream while whisking. Stir in the Parmesan cheese. Season to taste with salt and freshly ground black pepper. Mix the kale and croutons. Slice the chicken and place it on top of the kale. Drizzle over some of the dressing and serve the rest on the side. Garnish with shaved Parmesan.