Sift matcha into a matcha bowl (chawan) or other heatproof bowl and heat water to approximately 80 degrees C (hot, but not boiling).
Using a bamboo whisk or a hand frother, mix hot water and matcha until frothy. Set aside.
In a separate glass, mix coconut milk, ube extract, and maple syrup or other sweetener (if using). Set aside.
Fill a 12 oz glass with ice and pour in your ube milk.
Gently pour matcha on top. For a layered look, aim your matcha to hit an ice cube instead of directly into the liquid.
Mix your latte before drinking and enjoy!