Add the black sesame seeds into a food processor. Blend until the sesame seeds start to seep oil and thicken, about 2 minutes. Use a spatula to thoroughly scrape the paste from the walls and bottom of the food processor. Blend again until it forms a fine paste, 1 to 2 minutes. Scrape the paste from the walls and bottom.

Add sugar and white beans. Blend again until everything is fully mixed. If the paste is too thick to blend, you can add a very small amount of water. Transfer the paste to a bowl.

Heat half of the butter in a medium-sized skillet over medium heat until melted. Add the bean paste. Cook and stir until the butter is fully absorbed. Add the rest of the butter and cook until fully absorbed. Add the maltose if using. Cook and stir until the paste becomes quite dry and able to hold its own shape, 3 to 4 minutes. Transfer the sesame paste to a plate and spread it out. Let cool completely. You can store the sesame paste in the fridge to make it easier to handle later.

Combine golden syrup, kansui, vegetable oil and salt in a large bowl. Mix with a spatula until emulsified.

Add cake flour into the bowl. Gently fold the dough with a motion of scraping from bottom to top, like you are folding a cake dough. Do not stir the dough in a circular motion. It will toughen the dough.

When the flour is fully combined, shape the dough into a ball with your hands. The dough should be soft and a bit sticky but still hold its shape. Seal with plastic wrap. Let rest for 2 hours.

Once it has cooled off, divide the sesame paste into 30-gram portions if not using duck egg yolks. Or add half a duck egg yolk and some sesame paste onto a scale, so that it weighs 30 grams in total. Shape the sesame paste into a ball, then press the center to form a disk. Place the egg yolk in the center. Wrap the sesame paste around the yolk until fully covered, then shape it into a small ball. Place it onto a tray,

Once you have shaped all the mooncake fillings, cover them with plastic wrap and place them in the freezer. Wait until the balls harden so they’re easier to handle, 30 minutes or so. (*Footnote 3)

Once the mooncake dough is rested, scoop and measure 20g dough pieces. Shape each dough piece into a ball using your hands. Then place them onto a large tray. Cover the tray with plastic wrap to prevent the dough from drying out.

Preheat oven to 400°F (200°C). Line a baking sheet with parchment.

Place a dough piece onto your palm and use your thumb to flatten the dough from the center, until it forms a round disk that is thinner in the center and thicker on the outside. Place the black sesame filling in the center. Carefully wrap the dough around the filling. Spread the dough until it seals the filling in completely. The dough should be very soft but not sticky, and easy to shape, like soft clay. (*Footnote 4) If you find the dough too thick in some spots, pull off the dough and smooth the surface. It doesn't matter if the dough is so thin that it reveals the color of the filling. Roll the dough between your hands until the dough forms a smooth ball.

Slide the plastic pattern disc into the mooncake mold, pattern side down. Twist the handle to lock the pattern disc so it’s secure.

Dust both hands and the mooncake dough with a bit of cake flour, so it’s easy to release from the mold. Carefully place the mooncake into the mold.

Place the mold on a clean working surface and firmly press the handle until you cannot move it any further. Hold the handle down for at least 5 seconds so the pattern sticks. Then release the mold from the table and push the handle to release the mooncake onto the lined baking sheet. Work on the rest of the mooncakes and place them onto the tray, about 1” (1.5 cm) apart. Spray a very small amount of water onto the mooncakes to prevent the dough from cracking. Bake for 5 minutes until the patterns are set. The edges of the mooncakes should turn pale golden.

Meanwhile, make the egg wash by beating the egg yolk with milk (or water) in a small bowl.

Remove the mooncakes from the oven. Brush a thin layer of egg wash onto the surface of the mooncakes. Only brush the top surfaces, not the vertical (side) surfaces. Try to only brush it onto the arched pattern, and not the recessed concave area. If you accidentally brush too much egg wash and it fills in the pattern, use a small brush to clean the gaps and remove the excess egg wash.

Place the mooncakes back in the oven and lower the oven temperature to 350°F (176°C). Continue baking until the egg wash turns golden brown, 12 to 15 minutes.

Let mooncakes cool on the tray for 20 minutes before removing (*footnote 5). Then transfer to a plate to cool completely.

Once cooled completely, store the mooncakes in an airtight container. The mooncakes can be served after 24 hours, and they will look and taste better after 2 days. (Footnote 6)

Store the mooncakes in an airtight container in a cool dark area for up to 1 week, or in the fridge for 2 to 3 weeks, or in the freezer for up to 2 months. If stored in the fridge, let the mooncakes return to room temperature before serving. Thaw frozen mooncakes in the fridge overnight before serving.