In a food processor, combine the anchovy fillets, mayonnaise, and garlic. Process until smooth. Slowly add the remaining ingredients (except the salt and pepper), combining fully. Wait until the end to add any salt and pepper as most of the ingredients will add their own salt, and you may not need any.
Between the two sheets of parchment, use the flat side of a meat tenderizer to pound the chicken breast halves evenly, until they each are about ¼ inch thick.
Season both chicken breast halves with salt and pepper.
Gather the three wide dishes, and line them up side by side. In the first one, put the flour, garlic powder, and paprika. In the second dish, add the eggs, whisking well. In the third dish, add the panko and parmesan.
With one hand, dip a chicken cutlet into the flour, being sure to get flour into all the crevices. Shake any excess flour off gently, then dip the floured chicken into the eggs. With your other hand, move the chicken around until it is fully coated. Gently let the excess egg drip off, then dunk the chicken into the panko and parmesan mixture. Use your first (dry) hand to fully coat in the breadcrumbs. Set aside and bread the other chicken cutlet.
Heat the oil. When the oil is hot, gently add one chicken cutlet, and fry on each side for about 3-4 minutes, until golden brown and crispy. Remove the chicken and place it on the paper-towel lined tray. Repeat with the second cutlet. Slice the cutlets into bite-size pieces.
In a large bowl, dress the romaine with the Caesar dressing. Slather some Caesar dressing onto the roll, add the dressed romaine, then the sliced chicken, and top with parmesan and a squeeze of lemon juice.