Mash the anchovies with a fork in a medium sized bowl. Whisk in the remaining ingredients until smooth. Set aside.
Make the Chicken Cutlets
Using a sharp knife, slice the chicken breasts crosswise so that you have 4-5 thinner pieces.
Heat oil in a large skillet over medium-low heat. Pour flour into a shallow bowl, then beaten egg into a second bowl and bread crumbs into a third bowl.
Dredge each chicken breast in flour, then beaten egg mixture, then breadcrumbs. Place into the skillet. Cook until golden on each side, flipping after 6-7 minutes. Do not crowd the pan. Repeat the process with remaining cutlets.
Remove from the pan to rest on a wire rack.
Assemble the Sandwiches
Rinse and chop the romaine lettuce. Toss chopped romaine with some of the Caesar dressing to coat. Spread more Caesar dressing onto both insides of each ciabatta roll.
Place chicken cutlet onto the bottom of each ciabatta roll and top with some of the Caesar salad. Press the top of each ciabatta roll onto each sandwich. Enjoy!