Cut the honeydew in half. Use a small melon baller to scoop out balls from one half of the honeydew. Set them aside. Add the remainder of the honeydew to a blender.
Cut the other half of the honeydew into chunks and add them to the blender. Add coconut milk and sugar to the blender and blend until smooth. Transfer the blended honeydew milk to a large mixing bowl. Let it chill in the fridge until ready to serve.
Bring a medium pot of water to a boil. Add in the tapioca pearls and stir immediately to prevent clumping. Boil uncovered for 10 minutes.
Cover the pot, remove it from the heat, and let it sit for another 10 minutes until the tapioca pearls are translucent all the way through.
Drain the water with a fine mesh sieve and rinse the tapioca pearls in cold water. Add the cooked tapioca pearls to the chilled honeydew milk.
Stir to mix together. Serve cold by scooping the sago into individual bowls or glasses. You can stir in some ice cubes if you want it colder. Top with the honeydew melon balls or stir them into the pudding.