Pat the chicken dry and season all over with salt and pepper. Combine all the marinade ingredients, excluding the chicken, in a bowl. Whisk to combine until smooth. Add the chicken and toss to coat. Transfer to the refrigerator for at least 15 minutes or up to 24 hours.

Add the anchovy fillets and garlic to a food processor and pulse until minced. Add the egg yolks, lemon juice, and Dijon mustard and blend until completely combined and smooth. Add the extra virgin olive oil and Parmesan and blend until smooth and creamy. Add salt and pepper to taste and blitz one final time. Transfer to a jar and refrigerate until needed.

Bring a medium pot of water to a boil. Add the eggs and reduce heat to medium. It should still be bubbling, but not vigorously. Cook the eggs for 15 minutes. Transfer to an ice bath and then peel and chop. Refrigerate until needed.

Heat 1 tablespoon extra virgin olive oil in a large skillet over medium-high heat. Once hot, add the chicken in an even layer without moving for 5–6 minutes. Flip and cook for an additional 5–6 minutes. Continue cooking, flipping occasionally, until the chicken reaches 165ºF. Transfer to a cutting board and chop the chicken into bite-sized pieces.

As the chicken cooks, make the salad. Gather the Romaine lettuce, radishes, cucumbers, and chopped hard-boiled eggs in a bowl. Add the lemon juice and toss to combine. Sprinkle with salt and set aside.

Transfer the salad to a large serving platter and pile the chopped chicken on top. Enjoy!