Measure the flour, sugar, salt and yeast into the bowl of an electric stand mixer.

Lightly mix the ingredients together using the dough hook.

Add the egg to the bowl.

Slowly pour in the warm milk, and continue mixing until everything comes together into a rough dough.

Add the butter, one tablespoon at a time. Once the butter has been fully incorporated into the dough, add the next tablespoon of butter.

Once all of the butter has been added, continue kneading the dough on medium speed for about 15 to 20 minutes.

The dough is ready when it is soft and smooth, and no longer sticks to the side of the bowl. The dough will be somewhat sticky from the butter and egg.

Lightly oil a large mixing bowl.

Place the dough inside the bowl.

Cover the dough with a clean tea towel, plastic wrap, or a reusable bowl cover.

Leave the dough somewhere warm for 1 to 1.5 hours, or until the dough has doubled in size (see Kitchen Notes below).

During this time, make the Coconut Filling.

Just before the dough is ready, make the filling.

Place all of the ingredients into the bowl of an electric stand mixer, fitted with a paddle attachment (alternatively, you can do this by hand with a wooden spoon).

Beat the ingredients together until everything is well combined.

Portion the filling into 16 equal pieces. If you have some kitchen scales, weigh the filling and then divide this number by 16. This will be the weight of each piece of filling.

Roll each piece of filling into a log about 8 cm/3 inches long.

Line a 40 x 30 cm/16 x 12 inch sheet pan with baking paper.

Once the dough has doubled in size, gently remove the dough from the bowl.

Pat the dough into a round shape.

Portion the dough into 16 equal pieces. If you have some kitchen scales, weigh the dough and then divide this number by 16. This will be the weight of each bun dough.

Roll each piece of dough into a round ball. I do this by pulling the edges of the dough together into a tight ball.

Arrange the balls of dough on the sheet pan.

Set the balls of dough aside to rest for about 10 minutes, until they are slightly puffy.

Line a second 40 x 30 cm/16 x 12 inch sheet pan with baking paper.

Gently roll out a piece of dough with a small rolling pin, until you have a slightly oval shape, about 12 cm/5 inches in length.

Place a piece of filling in the middle of the dough.

Encase the filling inside the dough by pinching together the edges of the dough, and shaping the dough into a nice oval shape.

Place the assembled bun onto the sheet pan with the seam-side down.

Repeat the above steps with the remaining pieces of dough.

If you wish to create individual buns, space the pieces of dough a good 5 cm/2 inches apart. This is the more traditional way to bake the Chinese Coconut Buns.

If you wish to create adjoining buns, place the pieces of dough closer together (about 1 cm/1/2 inch apart). I find that baking the buns closer together creates buns with more height, and with a softer and fluffier interior.

Place the pan somewhere warm for about 30 minutes, or until the buns have risen and puffed up slightly.

During this time, make the egg wash and topping.

Beat all of the ingredients together until you have a thick, but soft, paste.

Transfer the paste to a small piping bag.

Cut a small piece off the end of the piping bag.

Preheat the oven to 180°C/350°F (without fan) with a metal baking tray on the middle shelf.

Gently brush each bun with some egg wash.

Pipe a line of the topping across the top and bottom of each bun.

Sprinkle some sesame seeds in the middle of each bun.

Place the pan of buns on the preheated baking tray.

Bake the buns for 15 to 20 minutes.

Check the buns at about 10 minutes, and if they are browning too quickly, cover them with a loose sheet of foil for the rest of the baking time.

The buns are cooked if an internal thermometer reads 85°C/185°F.

Gently remove the buns to a wire rack, and leave them to cool completely.