Add the chocolate chips to a double boiler over simmering water and stir until melted.
Stir in cocoa and sugar.
Remove from heat and whisk in 1/2 cup milk and stir until smooth.
Set aside and cool to room temperature.
In a blender add the remaining 1 cup of milk,the cooled chocolate, and the ice.
Blend on high speed until smooth.
Drizzle chocolate syrup in 2 chilled glasses.
Pour into two large glasses and top with whipped cream, chocolate curls, and a straw.