Prepare the Strawberry Puree: In a small food processor or blender, combine the frozen strawberries, granulated sugar, and lemon juice. Blend until completely smooth. Set aside.

Prepare the Matcha: Sift the matcha powder into a small bowl to prevent clumps. Whisk vigorously with a small amount of hot water (about 2 tablespoons) using a bamboo whisk or small whisk until a smooth, frothy paste forms with no lumps.

Assemble the Base: In the serving glass, spoon 2-3 tablespoons of the strawberry puree along the bottom edge. Add the ice cubes to fill the glass about halfway.

Mix the Milk: In a separate container, combine the milk and vanilla extract. You can shake this mixture or lightly whisk it to incorporate a little air.

Layer the Drink: Slowly pour the milk mixture over the ice, filling the glass almost to the top. The strawberry layer should remain mostly at the bottom.

Add the Matcha: Very slowly and carefully, drizzle the prepared matcha paste over the top of the milk layer. It should float slightly on top or swirl down gently.

Serve immediately. Instruct the drinker to gently stir before consuming to combine the layers.