Preheat the oven to 375°. Butter a 9-by-13-inch casserole dish.

Season the chicken cutlets evenly with 1 teaspoon salt and ½ teaspoon black pepper.

Heat a large skillet over medium heat; add 1 teaspoon butter and 4 of the chicken cutlets. Cook 2 to 3 minutes per side or until browned. (Chicken will not be cooked through the center.) Remove from the skillet and transfer to a plate. Repeat with 1 teaspoon butter and remaining chicken.

Add the ham to the drippings in the skillet, and cook over medium heat, stirring occasionally, until lightly browned, about 2 min. Remove the ham from the skillet and set aside.

Place 3 tablespoons of the butter in the same skillet over medium heat. Slowly whisk in the flour and cook, stirring, for 1 minute.

Slowly whisk in the milk and chicken broth, then add the cayenne, if you like. Bring to a simmer and cook, stirring often, until thickened, about 3 minutes. Remove from the heat. Stir in the mustard and ½ cup each of the Swiss and mozzarella until the cheese melts. Season with the remaining ½ teaspoon salt and ¼ teaspoon pepper.

Combine the panko, parsley, and remaining 1 tablespoon of melted butter in a small bowl. Mix well to coat.

Spoon 1 ½ cups of the cheese sauce in the prepared casserole dish. Arrange the chicken cutlets in the dish, overlapping slightly. Spoon the remaining sauce evenly over the chicken. Add browned ham. Top with remaining ½ cup each of the Swiss and mozzarella. Top evenly with the panko mixture.

Bake until golden brown and bubbly, and chicken is cooked through, 25 to 30 minutes.

Sprinkle with additional parsley and serve alongside steamed rice and green beans, if you like.