Heat the vegetable oil in a large pan over medium heat.
Add the finely chopped onion and cook until translucent.
Stir in the minced garlic and cook for another minute until fragrant.
In a bowl, combine the grated coconut with the coconut milk, salt, black pepper, and dried thyme (if using). Mix well.
Add the coconut mixture to the cooked onion and garlic. Stir to combine and let it cook for about 5 minutes, or until the mixture thickens slightly. Remove from heat.
If using taro leaves, clean them thoroughly and remove any tough stems. If using banana leaves, clean and soften them by briefly passing them over a flame or steaming them.
Place a large piece of taro or banana leaf on a flat surface.
Spoon some of the coconut mixture onto the center of the leaf.
Fold the leaf over the mixture, creating a parcel. Secure the parcel with kitchen twine or toothpicks if necessary. Repeat with the remaining mixture and leaves.
Place the parcels in a steamer basket or on a rack in a large pot with a small amount of water in the bottom. Steam over medium heat for about 30-40 minutes, or until the filling is cooked through and the leaves are tender.
Remove the parcels from the steamer and let them cool slightly before unwrapping.
Enjoy your meal!