Slice the chicken breasts horizontally into 4–6 thin cutlets.
Whisk the egg, milk, garlic powder, salt, and pepper in a bowl. Place breadcrumbs and panko in another bowl.
Dip chicken into egg mixture, then coat with breadcrumbs. Fry in 1-inch oil over medium-high heat until golden and crispy, about 5 minutes per side. Drain on paper towels.
Mix all garlic butter ingredients in a bowl. Spread inside the sliced bread and toast at 450°F for 3–4 minutes until golden.
Whisk all Caesar dressing ingredients until smooth.
Toss romaine with 3–4 tablespoons dressing.
Assemble the Chicken Caesar Sandwiches with toasted bread, crispy chicken, dressed lettuce, and extra Parmesan. Serve immediately.