Slice chicken breasts horizontally into thin cutlets. In a mixing bowl, whisk together egg, garlic powder, salt, and pepper. Dip each chicken piece into the egg mixture, then coat with breadcrumbs and panko.

Heat vegetable oil in a shallow pan over medium-high heat. Fry each side of the breaded chicken cutlets for about 5 minutes until golden brown. Let them drain on paper towels.

Mix softened butter, minced garlic, fresh parsley, and grated Parmesan in a small bowl. Spread the garlic butter on halved hoagies or baguettes. Toast in a preheated oven at 450°F for 3-4 minutes.

Whisk together mayonnaise, sour cream or Greek yogurt, lemon juice, Dijon mustard, anchovy paste, Worcestershire sauce, minced garlic, salt, and pepper in a medium bowl. Taste and adjust seasoning.

Layer crispy chicken cutlets on toasted hoagies, top with dressed romaine lettuce, and finish with additional Parmesan cheese. Close the sandwich and serve immediately.