Drizzle some chocolate syrup on the sides and top of 2 tall glasses.
Spread chocolate shavings on a plate and invert the glasses on the plate to rim them with the shavings. Freeze the glasses for 10 minutes.
Stir together instant coffee powder, sugar and warm water in a small bowl.
Add chilled whole milk, unsweetened cocoa powder, chocolate syrup, milk powder, chocolate ice cream, and the coffee mixture to the medium jar of a blender and blend for a minute.
Pour the coffee in the prepared glasses. Add some froth on top using a spoon.
Top with scoops of vanilla or chocolate ice cream. Drizzle chocolate syrup and chocolate shavings on top. Serve immediately.