Wash the lettuce thoroughly and refrigerate until crisp, at least 1 hour or more.
Set the oven to 190°C, air on and rack set to the middle of the oven.
Start with the croutons by adding them in a large bowl along with the granulated garlic, ½ tsp of salt and the oregano. Toss them with 2 tbsp of olive oil and place them in an oven-proof tin sheet to be baked until golden brown and crisp, about 15’, tossing them halfway. Remove from the oven and keep aside.
Change the oven settings by setting the oven to 250°C, grill/broiler, rack on the highest level.
In the meantime, cut the chicken breasts in a butterfly way so that you have ½cm thickness fillets. Brush them with 2 tbsp of olive oil and season them with the salt and pepper. Place the fillets in the same tin sheet that the croutons were made and grill them on each side for 4-5’ minutes. Take out of the oven and slice them into strips.
For the dressing, we place in a high-speed food processor, with the metal blade on, the anchovies paste, the egg yolks, mustard, garlic, lime or lemon juice, Worcestershire sauce, the grated Parmigiano Reggiano cheese, the remaining salt and pepper and blend. In the same way as you would make mayonnaise, pour slowly the olive oil aiming to thicken the sauce.
Take a large bowl and add the torn lettuce leaves. Pour ¾ of the dressing and toss well. Remove from the bowl to individual serving plates, add on top the cut chicken fillets and drizzle the remaining dressing. Finally, toss on top the croutons and the shaved Parmigiano Reggiano. Give a final crack of black pepper and enjoy.