Heat up coconut milk in a saucepan.
In a cup, add lime juice and cornstarch. Mix until dissolved.
Next add it to the hot coconut milk along with agar-agar, rice syrup, vanilla (and matcha if desired). Stir the mixture constantly until it begins to cook and thicken. Keep stirring and cook for approx. 1 minute more.
Then Remove from the heat and set aside. Allow to cool down until room temperature.
Pour the key lime filling into your prepared tart.
Let set in the fridge for at least 3 hours (or overnight) to firm up.
Decorate your tart with lime or lemon slices and red currants or other fruits/ berries before serving, if you like.