Whisk Greek yogurt, mayonnaise, 4-5 tbsp Parmesan, garlic powder, Dijon mustard, Worcestershire sauce, lemon juice, salt, and pepper into a smooth Caesar dressing. Set aside.
Season chicken cutlets with salt, paprika, and garlic powder. Dredge in seasoned flour, dip in seasoned eggs, and coat firmly in combined Panko, breadcrumbs, and Parmesan.
Shallow fry cutlets in 1/2-inch of hot oil for 3-4 minutes per side until golden brown and cooked through. Drain on a wire rack.
For the dipping sauce, melt butter in a pan over medium heat and sauté garlic for 1 minute. Add cream, cheddar, 50g Parmesan, salt, fresh cracked pepper, and cornstarch slurry.
Simmer sauce for 1-2 minutes until thickened. Remove from heat, let cool slightly, then stir in 2 tbsp of Caesar dressing.
Toss chopped Romaine lettuce with 2-3 tbsp of Caesar dressing.
Assemble burgers: Bottom brioche bun, Caesar dressing, first crispy chicken cutlet, Caesar lettuce, second chicken cutlet, Caesar lettuce, grated Parmesan, and top bun.
Serve immediately with french fries and warm Garlic Caesar Pepper Dipping Sauce.