Slice the chicken breasts horizontally to create thin cutlets, about ½ inch thick. Whisk together the egg and milk, seasoning with garlic powder, salt, and pepper. In a separate dish, pour in the breadcrumbs. Dip cutlets into the egg mixture and press into the breadcrumbs.

Heat vegetable oil in a skillet over medium-high heat until 350°F. Fry the breaded chicken cutlets for about 5 minutes on each side or until golden brown. Transfer to a paper towel-lined plate to drain excess oil.

Prepare the garlic butter by mixing softened butter with minced garlic and parsley. Slice the hoagie rolls and spread the garlic butter mixture on each cut side. Toast in a preheated oven at 450°F for 3-4 minutes until golden.

To prepare the dressing, whisk together mayo, Greek yogurt, Parmesan, lemon juice, Dijon mustard, anchovy paste, Worcestershire sauce, and salt. Toss the romaine lettuce with the Caesar dressing in a large bowl.

Assemble the sandwiches by layering the fried chicken cutlets on the toasted hoagie rolls, followed by the dressed lettuce and an extra sprinkle of Parmesan. Close with the top half and serve immediately.