Slice sponge cake into 3 layers using serrated knife, each about 1-cm thick (cover to prevent from drying).
Steam taro and purple sweet potato with pandan leaves for 20 minutes, until very soft.
Add 400 g of plain water to steamed taro and purple sweet potato, blend until smooth.
Combine thick coconut milk, mung bean starch and taro mixture, mix well, then strain into a thick base cooking pot (to prevent from burning).
Combine another 400 g of water, salt, sugar and agar-agar powder in a sauce pot, bring to the boil, cook until agar-agar has melted.
Add agar-agar mixture to taro mixture gradually while stirring. Cook mixture over medium heat until slightly thickened (about 2.5 minutes) , off the heat and continue to stir until smooth. Dip cooking pot in hot water and put on the lid (to prevent mixture from setting).
Rinse 9-inch/23-cm round baking pan with water, drain-off excess water (to help in unmoulding).
Pour 350 g of taro layer mixture into baking pan, swirl to coat the sides, put in 1 slice of cake, set aside for 4 minutes to allow taro layer to slightly set.
Pour 320 g of taro layer mixture over 1st slice of cake, top with 2nd slice of cake, set aside for 3 minutes until slightly set. Repeat the same for the 3rd slice of cake.
Pour 550 g of taro layer mixture over 3rd slice of cake and into the gap between the cake and baking pan, set aside until cooled.
When cooled, loosen the cake sides from baking pan with plastic knife.
Cover the baking pan, keep refrigerated for 5-6 hours or overnight until completely set.
Unmould and cut with plastic knife into slices.