Slice the chicken breasts horizontally to create thin cutlets. Whisk egg and milk with garlic powder, salt, and pepper, then coat chicken cutlets.

Heat vegetable oil in a skillet over medium-high heat. Fry chicken cutlets for about 5 minutes until golden brown, then drain on paper towels.

Mix melted salted butter, mayo, garlic, parsley, and Parmesan for the garlic butter spread. Spread on hoagies and toast in a preheated oven at 450°F for 3-4 minutes.

Combine mayo, sour cream, Parmesan, lemon juice, Dijon mustard, anchovy paste, Worcestershire sauce, and garlic in a bowl for the dressing. Whisk until smooth.

Layer fried chicken on toasted garlic butter bread, add romaine, drizzle with Caesar dressing, and sprinkle with extra Parmesan before topping with the other half of the bread.

Serve immediately and enjoy with sides of your choice, such as chips or fries.