Begin by preparing the oil dough. In a bowl, rub the cake flour with the leaf lard and chilled cubed butter. Knead gently until it comes together into a soft, pliable dough. Set aside.

For the water dough, mix the all-purpose flour and icing sugar in a large bowl. Add the leaf lard, chilled butter, and water. Knead the mixture until it forms a smooth, elastic dough that does not stick to your hands.

Divide both the water dough and the oil dough into 12 equal portions each. Cover with a damp cloth to prevent them from drying out.

Take one portion of the water dough and flatten it into a circular disc approximately 4 inches across. Place one portion of the oil dough in the center and enclose it fully with the water dough, pinching to seal. Repeat with the remaining portions.

Working one dough ball at a time, use a rolling pin to roll it into a long oval shape. Roll it up tightly from the short end, similar to rolling a Swiss roll. Rotate the rolled dough 90 degrees, and then roll it out again into an elongated oval. Roll it up once more tightly from the shorter edge.

Flatten each rolled dough with a rolling pin into a round disc about 4 inches in diameter. Spoon a portion of the mung bean paste filling into the center. Wrap the dough around the filling, pinching to seal and forming a ball. Shape as desired: either keep it round or gently press it into a flatter shape if preferred.

Preheat the oven to 350°F (175°C). Line a baking tray with parchment paper. Arrange the shaped biscuits seam-side down on the prepared tray, leaving a little space between each one.

In a small bowl, whisk the egg yolk and milk together until well combined. Brush the tops of the biscuits lightly with the egg wash. If desired, sprinkle a few white sesame seeds over the tops for added texture and flavor.

Place the tray into the preheated oven and bake for about 20 minutes, or until the biscuits turn golden brown and the tops are shiny and crisp. Remove from the oven and allow them to cool on the tray for about 1 minute before transferring them to a wire rack to cool completely.

Once completely cooled, store the Tambun Biscuits in an airtight container at room temperature. They will stay fresh for up to one week. If storing longer, refrigerate them to maintain their texture and flavor.