Bring 1 cup of water to a boil in a medium saucepan. Add the tapioca pearls and cook according to the package instructions, typically for about 15-20 minutes, until they are soft and chewy.
Once the boba is cooked, drain and rinse under cold water to stop the cooking process. Transfer the boba to a bowl and mix with 1 tablespoon of sweetener to sweeten. Set aside.
In a blender, combine the mango puree, brewed green tea, and the remaining sweetener. Blend until smooth. Taste and adjust sweetness if necessary.
Fill a serving glass about halfway with ice cubes. Add the sweetened boba pearls to the glass.
Pour the mango tea mixture over the boba and ice.
Gently pour the milk on top to create a layered effect. Stir the bubble tea before drinking to mix all the flavors together.