Begin by slicing the boneless, skinless chicken breasts into thinner cutlets for even cooking. In a mixing bowl, whisk together the egg and milk along with garlic powder, salt, and pepper. Set up another bowl with breadcrumbs. Dip each chicken cutlet into the egg mixture, coating it well, then transfer to the breadcrumbs, ensuring an even layer. Fry the breaded cutlets in hot oil at 350°F until they reach a golden brown color, about 5 minutes on each side.

While the chicken is frying, prepare the garlic butter. In a small bowl, mix melted salted butter with mayonnaise, minced garlic, finely chopped parsley, and grated Parmesan cheese until well combined.

Preheat your oven to 450°F. Split the hoagies or baguettes lengthwise and generously spread the garlic butter mixture inside each half. Place them on a baking sheet and toast in the oven for about 3-4 minutes, keeping a close eye to prevent burning.

In a separate mixing bowl, combine mayonnaise, sour cream (or Greek yogurt), fresh lemon juice, Dijon mustard, anchovy paste, Worcestershire sauce, and grated garlic. Whisk until smooth and creamy, seasoning with salt and pepper to taste.

On the toasted garlic butter-coated bread, layer the crispy chicken cutlets followed by a generous portion of the dressed romaine lettuce. Sprinkle extra grated Parmesan cheese on top for flavor. Close the sandwiches and serve immediately.