Peel the bananas and freeze them for 3 hours or until solid.
Drizzle the agave syrup on a small plate and sprinkle the desiccated coconut on another small plate. Dip the rim of two tall serving glasses first into the agave syrup, then into the coconut. Set the glasses aside.
Add the light rum and frozen strawberries to a blender and blend until smooth.
Pour the mixture into the glasses to the halfway mark.
Rinse the blender out, then add the coconut rum, pineapple juice, coconut cream, frozen bananas, and ice and blend until smooth and creamy.
Fill the glasses to the top with the banana mixture.