Add the fresh blueberries, water, and maple syrup to a small saucepan. Heat the mixture over medium heat and stir until the blueberries soften and burst. Lightly crush them with a spoon to release their juices. Let the mixture cool slightly.
Purée the mixture until smooth using an immersion blender and set aside.
Sift the matcha powder into a bowl to avoid clumps. Pour ½ cup of hot (not boiling!) water over it. Whisk vigorously with a matcha whisk or milk frother until the matcha is frothy and smooth.
Pour the blueberry purée into a glass. Fill it about one-third full with ice cubes. Now pour in the milk of your choice, but leave room for the matcha. Slowly pour the matcha on top to create a nice layered effect.