Place milk, cocoa powder and sugar in a small saucepan.
Heat over medium-low heat, until steaming but not boiling.
Add chocolate chips and stir constantly until melted and fully combined.
Remove from heat, stir in vanilla extract.
Allow the chocolate mixture to cool slightly, then transfer it to a blender. Add the ice cubes and blend on high speed until thick and frosty.
Pour the frozen hot chocolate into glasses and garnish with whipped cream, chocolate shavings, or any other desired toppings.
*You can adjust the amount of ice cubes based on your desired thickness and frozen texture. Start with 1 cup of ice and add more if you want it thicker and more frozen.