01 - Place chicken breasts between sheets of plastic wrap and pound to an even 1/2-inch thickness. Season both sides with salt and black pepper.
02 - In a large mixing bowl, combine the chicken and buttermilk. Allow to marinate for at least 20 minutes or up to 4 hours in the refrigerator.
03 - In a shallow dish, mix together flour, panko breadcrumbs, garlic powder, paprika, and cayenne pepper.
04 - Remove chicken from the buttermilk, letting excess drip away. Dredge each breast thoroughly in the flour-breadcrumb mixture, pressing to ensure an even coating.
05 - Heat vegetable oil in a large skillet over medium-high heat to 350°F. Fry chicken breasts for 3 to 4 minutes per side, until golden brown and fully cooked. Transfer to paper towels to drain.
06 - In a small bowl, whisk together mayonnaise, grated Parmesan, Dijon mustard, minced anchovy (if using), minced garlic, lemon juice, and a pinch of salt and black pepper until smooth.
07 - Lightly toast the brioche or hamburger buns until golden.
08 - Spread Caesar dressing generously on both halves of each bun. Layer with Romaine lettuce, tomato slices, crispy fried chicken breast, and extra Parmesan if desired. Close with the top bun and serve immediately.