Whisk Greek yogurt, mayonnaise, 4-5 tbsp Parmesan, garlic powder, Dijon mustard, Worcestershire sauce, lemon juice, salt, and pepper until smooth to make the Caesar dressing. Set aside.
Season chicken cutlets with salt, paprika, and garlic powder.
Dredge cutlets in seasoned flour, dip into seasoned whisked eggs, and coat firmly in combined Panko, classic breadcrumbs, and Parmesan.
Heat 1/2-inch of oil in a skillet over medium-high heat. Fry cutlets for 3-4 minutes per side until golden brown and cooked through. Drain on a wire rack.
In a bowl, toss chopped Romaine lettuce with 2-3 tbsp of the Caesar dressing.
Assemble burgers: Spread Caesar dressing on toasted bottom brioche bun, layer with first crispy cutlet, Caesar lettuce, second cutlet, Caesar lettuce, grated Parmesan, and top bun. Serve hot!