Bring water to a boil.
Add loose leaf tea and steep for 5-10 minutes.
Remove tea leaves.
Add sugar and stir to dissolve completely.
Let the tea-flavored syrup cool to room temperature.
Add bananas and syrup to a blender and blend until smooth.
Add chocolate and vanilla extract.
Blend all ingredients together until smooth.
Pour mixture into a freezer safe container.
Freeze for approximately 12 hours.
Spoon into sorbet cups and enjoy!