01 - Place chicken breasts between sheets of plastic wrap and pound to even thickness, approximately 1/2 inch; season both sides with salt and black pepper.
02 - Combine chicken breasts and buttermilk in a bowl. Marinate in the refrigerator for at least 20 minutes or up to 4 hours.
03 - In a shallow dish, blend flour, panko breadcrumbs, garlic powder, paprika, and cayenne pepper until evenly combined.
04 - Remove chicken from buttermilk, allowing excess to drip off. Thoroughly coat each breast in the breading mixture, pressing to ensure an even layer adheres.
05 - Heat vegetable oil in a large skillet over medium-high to 350°F. Fry chicken 3–4 minutes per side until golden brown and cooked through, then transfer to paper towels to drain.
06 - Whisk mayonnaise, grated Parmesan, Dijon mustard, minced anchovy (if using), minced garlic, lemon juice, and a pinch of salt and pepper until smooth and creamy.
07 - Lightly toast brioche or hamburger buns until golden.
08 - Spread Caesar dressing on each bun half. Layer with Romaine lettuce, tomato slices, fried chicken breast, and extra Parmesan if desired. Cap with the other bun half and serve immediately.