Thoroughly rinse the split mung beans, and soak them in water for 8+ hours or overnight.
Drain the mung beans and place them into a clean, heat-safe bowl. Place a steamer rack into a large pot and pour in the water.
Place the bowl of mung beans onto the steamer rack, then cover the pot.
Bring the water to a boil over high heat, then reduce the heat to medium and steam for 40 minutes. (Alternatively, use the 'Steam' option in an Instant Pot for 12 minutes.) The mung beans are done when you can easily mush them with your fingers.
Mash the mung beans into a smooth paste and transfer to a skillet along with the sugar and oil. Using a spatula, stir and fry the mixture over medium-low heat for 5-10 minutes, or until the paste easily sticks together.
Turn off the heat and let the mixture cool. At this point, feel free to add the taro powder to 2/3 of the mixture.
Divide it into 50-gram pieces. Place each piece into your mooncake mold and press into mooncakes. (Alternatively, press the entire mixture into a square container, then slice it into squares.) Enjoy!