Place the chicken breasts on a cutting board and slice them horizontally into 4–6 thin cutlets, depending on their size.
In a shallow bowl, whisk together the egg, a splash of milk, garlic powder, salt, and black pepper.
Combine the regular breadcrumbs and panko in a second shallow bowl.
Dip each chicken cutlet into the egg mixture, allowing excess liquid to drip away. Transfer it to the breadcrumb mixture and press the crumbs firmly onto both sides.
Pour enough vegetable oil into a large skillet to create a shallow layer. Heat over medium to medium-high heat.
Carefully add the breaded chicken without overcrowding the pan. Fry until deeply golden and crispy on both sides and the center reaches 165°F (74°C). Depending on thickness, this should take about 5–7 minutes total.
Transfer the cooked chicken to a wire rack or paper towel-lined plate and allow excess oil to drain.
Preheat the oven to 450°F (230°C), or set the broiler to high.
To prepare the garlic butter, combine the softened or slightly melted butter, mayonnaise, minced garlic, parsley, and Parmesan in a small bowl.
Split the bread lengthwise and generously spread the garlic butter over the cut sides.
Place the bread cut-side up on a baking sheet and toast for about 3–4 minutes, watching carefully, until golden around the edges.
Prepare the Caesar dressing by whisking together mayonnaise, sour cream or Greek yogurt, Parmesan, lemon juice, Dijon mustard, anchovy paste, Worcestershire sauce, grated garlic, salt, and pepper.
Place the shredded romaine in a large bowl. Add 3–4 tablespoons of dressing and toss until the lettuce is lightly and evenly coated.
Assemble the Chicken Caesar Sandwiches by placing crispy chicken cutlets onto the toasted garlic bread.
Top generously with the dressed romaine and freshly grated Parmesan.
Add a little extra Caesar dressing if desired, close the sandwiches, and serve immediately while the chicken is crispy and the bread is warm.