At least 2 hours before making the buns, prepare your pastry cream or custard following the instruction in our Kagecreme recipe, or whichever custard you are using. Place in the fridge to cool down.
Heat the milk, in the microwave or a saucepan, until it is "fingervarm" (finger warm), meaning it should feel warm to the touch but not hot. Add your active dry yeast/fresh yeast and 1 tbsp of sugar, stir, and leave it for 5-10 minutes until the mixture starts to bubble up, meaning your yeast is alive and not expired. If using instant yeast, you do not need to do this step; you can add the yeast directly to the mixing bowl with everything else.
Add the salt, remaining sugar (0.5 tbsp), cardamom, and egg to a large bowl/bowl of a stand mixer and mix well. Once the yeast mixture has bubbled up a bit, add it to the egg mixture. Mix together.
Slowly add the flour and softened butter, mixing with a wooden spoon or the dough hook on a stand mixer until the dough starts to come together.
Knead until smooth and elastic, about 10 minutes. Use a stand mixer if you would prefer! Add more flour if the dough is too sticky - if it sticks to the sides of the bowl or is really sticking to your hands, you need a little bit more flour! The dough should be soft and smooth, not too sticky nor too dry.
Cover the dough with cling film or a clean dishtowel and place in the fridge overnight for 8 hours, or let rise at room temperature (if room temp is very cold wherever you are, put it in a warm place, i.e. under a light) for 45 minutes to an hour or until doubled in size.
Once your dough has doubled in size, shape it into 10 balls. Roll each ball on an unfloured surface to close any seam along the bun.
Place the buns on two lined baking sheets (with parchment paper or a silicone mat), 5 buns on each sheet.
Cover and let rise for about 15-20 minutes. In the meantime, preheat your oven to 390 degrees F (200 degrees C) - you won't need the oven for at least 15 more minutes after this, so adjust accordingly if your oven heats up very quickly.
After 15 minutes, we are going to create a well in each roll for the pastry cream filling. We usually press down into the middle with our fingertips, and use the bottom of a small glass (like a shot glass) to help even out the indentation.
It should look sort of like a donut but the hole is not fully punched through. The size of the indentation should be at least the size of a US quarter. After you've pressed an indent into each bun, cover and let rest for another 15-20 minutes.
After 20 minutes, press down the indent again to make room for the pastry cream. Egg wash the buns.
Spoon pastry cream into each well in the buns (around1-2 tbsp in each bun) - we use almost a whole portion of pastry cream for this.
Bake for 10-12 minutes. We bake both baking sheets at once, but rotate them halfway! You can also bake the sheets one at a time for more even cooking!
After they are done baking, transfer to a wire rack and let cool for at least 30 minutes.
Prepare a runny icing by mixing together powdered sugar and water. We don't usually measure these ingredients, but we probably used around 3/4 cup of powdered sugar - the goal of the icing is to create a sticky surface for the coconut to adhere to!
Brush the buns with the icing using either a brush or just a spoon, avoiding brushing the custard - you can also dip the buns in the icing, but we like to avoid putting icing on top of the custard so you can still see it!
Add shredded coconut to a plate. Dip the iced part of the buns in the shredded coconut or sprinkle over the top, whichever way you prefer!
Enjoy! We store these buns in the fridge for 2-3 days after baking.