In a large bowl, whisk together butter, mustard, and garlic. In another bowl, mix panko, parmesan, and parsley.
One at a time, turn chicken breast halves in butter mixture to coat completely. Dip rounded side of each breast in panko mixture. Place breasts crumb side up in a 10- by 15-inch baking pan.
Bake chicken in a 500° oven until crumbs are golden and breasts are no longer pink in center of thickest part (cut to test), about 15 minutes. Place 1 or 2 breast halves on each dinner plate. Accompany with Dijon sauce.
Dijon sauce. In a bowl, mix 1/2 cup mayonnaise, 1/4 cup Dijon mustard, 1/2 to 1 tablespoon Asian sesame oil, and 1 teaspoon soy sauce. Makes 3/4 cup.