Gently place the small tapioca pearls in 4 cups cold water and soak overnight. Don't stir or disturb.
Bring the 2 1/2 cups milk to a boil.
Meanwhile, scrape the vanilla seeds from the pod. Crush the lemongrass stalk to release the natural flavors. Peel the fresh ginger and cut into 2 tablespoons of rings. Place all of this into the hot milk and leave covered for half hour to steep, off the heat.
Strain out the milk infusion, and add the remaining 1/2 cup of milk to make up for the loss. Add the sugar and bring back to a boil. Strain the tapioca pearls and gently place into the hot milk. Gently stir with a rubber spatula and cook on medium heat for 3 to 5 minutes, stirring occasionally to avoid lumps. The tapioca is cooked once it looks translucent.
Warm up the coconut milk separately and add in at the end of cooking. Transfer to a container, place plastic on the top and refrigerate until cool, ideally overnight.
Once the pudding is cooled it will naturally set with the tapioca starch. Place into serving bowls and garnish with the fruits and the toasted coconut.