In a mason jar, combine egg yolks, anchovy filets, minced garlic, sea salt, and lemon juice. Blend for about 30 seconds until well mixed. Gradually pour in the avocado oil while blending continuously to create a smooth emulsion. Add the remaining lemon juice, black pepper, and pesto, then blend again until creamy.

In a large mixing bowl, chop the romaine lettuce into bite-sized pieces. Add in half of the grated Parmesan cheese, shredded rotisserie chicken, and the Castelvetrano olives. Toss to ensure even distribution.

Pour the creamy pesto dressing over the tossed ingredients and use tongs to coat all items evenly.

Arrange the salad in serving bowls or on a platter. Top with remaining Parmesan cheese and black pepper. Optionally, add croutons.