Take the milk out of the refrigerator to take off the chill.

Place the chocolate chips in a bowl over a double boiler. Turn the heat down to low and heat just enough to melt the chocolate. Add the sugar and cocoa powder and mix to combine.

Slowly whisk in the milk. The mixture should look like a concentrated chocolate milk. Let cool to room temperature.

Combine the chocolate base and the ice in a blender and mix until lush and it's similar consistency to an icee.

Pour the frozen hot chocolate into a chilled goblet. Whisk the heavy cream with the powdered sugar until it reaches stiff peaks. Top the drink with the whip and garnish with the chocolate shavings.