Bring 1 cup of water to a rolling boil in a medium saucepan. Gently add the tapioca pearls and cook according to the package's instructions, typically around 15-20 minutes, until all pearls are fully translucent and have a soft, chewy texture.
Once cooked, drain the boba and rinse under cold water to stop the cooking process. Sweeten the boba by mixing in 1 tablespoon of your chosen sweetener while still warm.
Sift the matcha powder into a bowl to remove any lumps. Add 1 cup of hot water (not boiling, ideally around 175°F or 80°C). Whisk vigorously in a zigzag motion until the matcha is fully dissolved and a light foam appears on the surface.
Stir in the remaining sweetener to the matcha mixture until dissolved. Allow it to cool to room temperature, or chill in the refrigerator to speed up the process.
Place ice cubes in a serving glass. Add the sweetened boba pearls over the ice.
Pour the cooled matcha over the boba and ice.
Top off with milk, adjusting the amount to your taste. Stir the bubble tea well to combine all ingredients into a refreshing, frothy beverage.