Soak the mung beans in hot water for about 1 hour, then cook until soft. Blend with water until smooth. Cook the mixture in a pan with the cornstarch slurry, add the sugar, and stir for about 25 minutes until thickened. Let cool, then shape into equal-sized balls.

For the oil dough:
Mix the all-purpose flour with the oil. Knead until smooth, then divide into equal portions. Cover and set aside while you prepare the main dough.

For the main dough:
Mix the all-purpose flour, cake flour, and baking powder (1).
In a separate bowl, dissolve the sugar and salt in warm water, then add the oil (2).
Pour (2) into (1) and mix until just combined, about 5 minutes, until the dough is smooth and elastic. Divide into equal portions.

Roll out a piece of main dough, place a piece of oil dough in the center, and roll out again. Roll up both doughs into a ball, then roll out again (this step can be tricky—search for 'how to make bánh pía dough' for visuals). Place a filling ball in the center, pinch the edges to seal, hold for 5-10 seconds, then roll into a ball and gently flatten.

Mix egg yolk with a little water. Brush the tops of the pastries and air fry at 356°F (180°C) for 17-20 minutes. Let cool before serving.