Place the chicken breasts on a clean cutting board. Carefully slice each breast horizontally into thin cutlets, making approximately 4–6 pieces depending on the size of the chicken.
In a shallow bowl, whisk together the egg, a splash of milk, garlic powder, salt, and black pepper.
In a second shallow bowl, combine the regular breadcrumbs and panko.
Dip each chicken cutlet into the egg mixture, allowing excess to drip away. Coat thoroughly in the breadcrumb mixture and gently press the crumbs onto the chicken.
Pour enough vegetable oil into a heavy skillet for shallow frying and heat over medium to medium-high heat.
Working in batches to avoid overcrowding, fry the chicken until deeply golden, crisp, and completely cooked. The thickest part should reach an internal temperature of 165°F (74°C).
Transfer the crispy chicken cutlets to a wire rack or paper towel-lined plate and set aside.
Preheat the oven to 450°F (232°C), or prepare the broiler. Combine the butter, mayonnaise, minced garlic, parsley, and Parmesan in a small bowl.
Split the bread lengthwise. Spread the garlic butter generously over the cut sides.
Toast for approximately 3–4 minutes, watching carefully, until the bread is golden around the edges and the Parmesan garlic butter is fragrant.
To prepare the Caesar dressing, whisk together the mayonnaise, sour cream or Greek yogurt, Parmesan, lemon juice, Dijon mustard, minced capers, halal-friendly Worcestershire-style sauce or soy sauce, grated garlic, salt, and black pepper until creamy.
Place the chopped romaine in a large bowl. Add 3–4 tablespoons of dressing and toss until the lettuce is lightly and evenly coated.
Assemble the Chicken Caesar Sandwiches by placing crispy chicken cutlets on the toasted bread. Add a generous portion of Caesar-dressed romaine and finish with freshly grated Parmesan.
Add a little extra Caesar dressing if desired, close the sandwiches, and serve immediately while the chicken and bread are still crisp.