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