Place dried coconut in blender carafe and add 4 cups just-boiled water. Allow to soak for 30 minutes and then blend on highest speed for two minutes. Set aside until cool enough to handle.
Once cooled, strain through a nut milk bag or fine sieve into bowl. Add sugar and stir to dissolve. If not ready to proceed right away, milk can be stored, covered tightly, in the refrigerator. Otherwise, continue with next step.
Place milk in a saucepan and heat over medium-low flame. Add tapioca starch and whisk until well dissolved.
Meanwhile, in a second saucepan, bring ½ water to a boil and add agar agar powder. Whisk and simmer until well dissolved, then pour into the heated coconut milk.
Allow to cool, whisking occasionally, to 110°F. Add starter, whisking again to evenly distribute, and pour milk into a glass container and incubate at 110°F using the method of your choice.
When incubation is complete, move jar to the refrigerator to chill and halt culturing, at least six hours. Yogurt is now ready to eat.