Prepare the Chicken - Place one of the chicken pieces between two plastic sheets or in a large plastic bag. Use a meat tenderizer and flatten it to an even thickness, about ½-inch thick. Repeat with the remaining piece.
Mix the Seasonings - In a small bowl, combine ¾ teaspoon salt and ½ teaspoon black pepper. Evenly season both sides of the chicken with the mixture.
Cook the Chicken - Heat a large skillet or grill pan over medium heat. Add olive oil, and heat until hot and shimmering but not smoking. Add the chicken and press down into the pan for maximum contact. Cook until golden brown, about 5 to 7 minutes. Flip and cook until the internal temperature reaches 160 to 165ºF (71 to 74ºC) on a meat thermometer, about 5 to 7 minutes.
Rest then Slice - Rest the chicken for 10 minutes. Once cool enough to handle, slice the meat against the grain. Set aside or refrigerate until ready to serve.
Make the Croutons - Heat the oven to 375ºF (191ºC). In a medium bowl, combine bread cubes, olive oil, salt, black pepper, and Italian seasoning (if using). Spread into a single layer on a sheet pan. Bake for 10 minutes, stirring halfway through. Bake for another 2 to 4 minutes until golden brown, dry, and crunchy. Cool on the sheet pan for 10 minutes.
Make the Anchovy Paste - On a cutting board, chop the anchovy fillets, minced garlic, and ¼ teaspoon salt together. Use the side of the knife to mash into a paste.
Make the Caesar Dressing - In a medium-sized bowl, whisk together the anchovy paste, mayonnaise, mustard, lemon juice, zest, ½ teaspoon salt, and ¼ teaspoon black pepper. Gradually whisk in olive oil until a thickened, smooth emulsion forms. Whisk in the parmesan cheese.
Dress the Salad - Add romaine lettuce to a large bowl and ¼ cup of dressing. Gently toss to combine. Add more to your liking or serve on the side.
To Serve - Top the salad with sliced chicken, more parmesan cheese, black pepper, and croutons.
Notes
Dressing Yield: Makes about ¾ cup of dressing
Using Raw Egg Yolk: A classic Caesar uses raw egg yolk. Substitute the mayonnaise with 1 pasteurized large egg yolk.
Using Anchovy Paste: 1 tablespoon (15g) of anchovy paste can be substituted for whole anchovies.
Storing: The undressed salad and dressing can be covered and stored separately in the refrigerator for up to 3 days. Store croutons in an airtight container at room temperature for up to 2 weeks.