Combine all the green layer batter ingredients in a bowl. Strain through a sieve and let the batter rest for 15 minutes.

Soak the mung beans overnight, then steam until cooked. Blend the cooked mung beans with the remaining white layer batter ingredients until smooth, then strain through a sieve. Let the batter rest for 15 minutes.

Brush a mold with vegetable oil. Set up a steamer. Pour the first layer of green batter into the mold, cover, and steam for about 5 minutes. Add the second layer with the white batter, cover, and steam for 2 minutes. Add a third layer of green batter, cover, and steam again. Check doneness by inserting a toothpick—if it comes out clean, the cake is done. Remove from the steamer. Repeat with the remaining batter and molds.