Sift the matcha powder through a fine-mesh strainer into a small bowl to eliminate clumps.
Pour the hot water (not boiling) over the sifted matcha powder.
Whisk vigorously in a zigzag motion using a bamboo whisk (chasen) or an electric frother until the powder is fully incorporated and a fine froth forms on the surface.
Incorporate the liquid sweetener into the matcha concentrate if desired.
Fill a glass with ice cubes and pour the cold milk over the ice.
Slowly pour the prepared matcha concentrate over the milk to achieve a layered effect.
Stir gently with a straw or spoon before drinking to integrate the flavors.