Over medium low heat, combine half & half, white chocolate, peppermint extract and vanilla in a medium saucepan, stirring occasionally. Cook 15 minutes or until chocolate is melted and heated through.
Beat whipping cream in a bowl at high speed until thickened. Add powdered sugar and continue beating until soft peaks form.
Pour hot chocolate into mugs; top with whipped cream and peppermint candies, if desired.