In a small saucepan, combine the chocolate, granulated sugar and cocoa powder. Whisk in 1 cup milk and cook over medium heat, whisking constantly, until smooth, about 4 minutes. Remove from the heat, whisk in the remaining 1 cup milk and refrigerate for 1 hour.
Pour the warm caramel sauce into a squeeze bottle and drizzle about half into the mugs or goblets so that it sticks to the sides.
In a medium bowl, beat the heavy cream with the confectioners' sugar until it forms soft peaks.
Using a blender, process the ice and chilled chocolate mixture until smooth. Pour into the glasses. Top with the whipped cream and the remaining caramel sauce. Serve with straws and spoons.