Sift 1 cup confectioners' sugar, 1/4 teaspoon ground cardamom and 1/2 cup cocoa powder into a bowl. Bring 6 cups milk to a simmer over medium heat. Whisk in the cocoa mixture until smooth. Fold 1/2 teaspoon orange zest into 1 cup whipped cream. Divide the cocoa among 6 mugs. Top with the whipped cream.