Add the coconut flakes to a coffee grinder and blitz a few times, until it's ground up. (Be careful not to over pulse).
Combine the coconut flakes with the beaten egg, sugar, butter, coconut and vanilla extract.
If making a matcha version: add matcha powder to the coconut flakes, egg, sugar, butter, coconut and vanilla extract.
Give the mixture a stir to combine, and then cover with a lid.
Place into the fridge to firm up, about 20-30 minutes.
Divide the filling into 12 equal portions.
Make the bun dough:
First, make the tangzhong by combining 25g flour and 120ml water in a small saucepan.
Bring a low simmer over medium heat and constantly whisk until the mixture becomes gluey and paste-like.
Remove from heat and let it cool to room temperature.
In a bowl, combine the warm coconut milk with the active dry yeast and let it foam up and become bubbly.
In a stand mixer bowl fitted with a dough hook attachment, add the flour, sugar, salt, egg, oil, tangzhong and the yeast mixture and knead until the dough becomes shiny and elastic.
Transfer the dough to a lightly greased bowl, cover, and let it double in size in a warm location.
Make the butter topping:
Combine the butter, cake flour, and powdered sugar in a small bowl and give it a mix.
Transfer the mixture into a small piping bag, fitted with a round tip.
Place it in the fridge for 15-20 minutes if the butter mixture oozes a bit and is too warm.
Note: If you don’t have salted butter, you can use unsalted butter, just add a little pinch of salt.
Assemble the buns:
Once the dough has risen, divide the dough into 12 equal portions.
Roll the dough out into a long oval about 6″ in length and 2″ wide.
Place a portion of coconut filling along the centre of the dough, leaving a small border on each side.
Pinch the long edge seam together and tuck in the ends.
Place the buns seam-side down on a large baking tray lined with parchment paper.
Repeat with the remainder.
Cover the buns with a slightly damp cloth and let them rise in a warm location, until slightly puffy.
Bake the buns:
Preheat oven to 350°F.
Once the buns have risen, make an egg wash by beating 1 egg in a small bowl.
Lightly brush the tops of the buns with egg wash and sprinkle sesame seeds on top.
Squeeze two “lines” of butter topping (about 1″ from both the top and bottom edges) on the buns.
Bake the buns at 350°F for 18-20 minutes, until lightly golden in colour.
Make the sugar glaze:
Combine 1 tablespoon of water with 1 tablespoon of sugar in a small bowl. Set aside.
Remove the buns from the oven and use a clean pastry brush to brush the top of each bun with the sugar glaze.
Turn off the oven and pop the buns back into the oven for 1-2 minutes to set the sugar glaze.
Remove the buns from the oven and transfer them to a cooling rack to cool.