Rinse the mung beans, then soak them in water for 4 hours. Drain thoroughly.
Transfer the soaked beans to a saucepan, cover with fresh water, and cook over medium heat until the beans are completely tender and can be easily crushed with a spoon. Drain well and allow to cool slightly.
Transfer the cooked mung beans to a blender. Add the tapioca starch, rice flour, sugar, coconut milk, vanilla, salt and oil. Blend until completely smooth, stopping to scrape the blender as needed.
Place the pandan leaves and water in a blender and blend until the leaves are fully broken down. Strain the liquid through a fine-mesh strainer, pressing firmly to extract as much liquid as possible. Discard the solids.
Pour the pandan juice into a blender pitcher along with the tapioca starch, glutinous rice flour, sugar, coconut milk, salt and oil to the pandan liquid and blend until smooth.
Prepare a steamer and bring the water to a steady boil over medium-high heat. Lightly oil a heatproof pan suitable for steaming. Stir each batter gently before using, as the starches will settle.
Pour a thin layer of the mung bean batter into the prepared pan. Place the pan in the steamer, cover, and steam for 4 minutes, until the surface is set and no longer liquid. Remove the lid carefully to prevent condensation from dripping onto the cake. Pour a layer of the pandan batter over the set mung bean layer. Steam for 4 minutes, until set. Continue alternating layers, stirring each batter before pouring, steaming each layer for 4 minutes, and keeping the layers thin and even.
After the final layer is added, steam for an additional 10 minutes to ensure the cake is fully cooked through.
Remove the pan from the steamer and let the cake cool completely to room temperature. Once fully cooled, cut into portions with a well oiled knife before serving.