Place the strawberries on a cutting board and chop coarsely. Add the sugar on top of the strawberries and continue to chop until the strawberries are finely minced and muddled. Set aside.
Place the matcha powder in a small bowl or spouted measuring cup. Add half the boiling water to the matcha and whisk until there are no more clumps and the mixture is completely smooth. Add the remaining hot water and continue whisking until the mixture is smooth. Set aside
Divide the strawberry puree into 2 12-ounce cups. Fill the cup ¾ of the way with ice.
Slowly add the milk on top of the strawberries, filling the cups about ¾ of the way full.
Finally, slowly pour the matcha on top of the milk. Stir with a straw to combine and enjoy immediately.
Notes
Storage Tip: While this drink is best made and then enjoyed right away, you can make a double (or triple!) batch of the strawberry puree and keep it in the fridge for up to five days.