Slice the chicken breasts into thin cutlets and whisk together egg, milk, garlic powder, salt, and pepper in one bowl. Place breadcrumbs in another bowl.

Dip each chicken cutlet into the egg mixture, then coat with breadcrumbs. Heat vegetable oil in a pan over medium heat to 350°F and fry for about 5 minutes on each side until golden brown. Place on paper towels to soak excess oil.

Melt butter in a small bowl and mix with mayo, minced garlic, and chopped parsley. Preheat the oven to 450°F and spread the garlic butter mixture on cut sides of the hoagies or baguettes. Toast for 3 to 4 minutes until golden.

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

Assemble by layering the crispy chicken cutlets on the toasted hoagie half, add chopped romaine dressed in Caesar dressing and sprinkle with Parmesan. Top with the other half of the bread.