Place coffee in filter in brew basket of coffee maker. Place sugar in empty pot of coffee maker. Add water to coffee maker; brew as directed. Stir in peppermint extract.
Microwave half-and-half and chocolate in medium microwavable bowl on HIGH 2 to 3 minutes or until heated through, stirring halfway through cook time. Stir until chocolate is completely melted and mixture is smooth. Stir into brewed coffee.
Pour into serving cups. Top with whipped cream and chocolate curls, if desired.