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.
Learn How to Make Creamy Caramel Sauce—Quick!