Activate the yeast if using active dried yeast:
Weigh out 13g of yeast granules, a pinch of sugar and 250ml warm whole milk (heated to 37 degrees -finger warm, but not hot). Whisk together, cling film the bowl and leave in a warm place to activate for about 15 minutes.
If using fresh yeast, add the warm milk to the mixing bowl and add the yeast, stir until dissolved.
Using the dough hook in your stand mixer, start the machine and add the cooled, melted butter – allow to combine with the yeast for a minute or so, then add the sugar. Again, allow to combine for a minute.
In a separate bowl, weigh out 400g bread flour, add the salt and the cardamom and mix together. Start adding the flour and spice to the mixture in the main bowl, bit by bit. Add the ½ egg. Keep kneading for about 5 minutes if using a mixer (longer if doing it by hand).
You may need to add more flour – you want the mixture to end up still a bit sticky, but not so much that it sticks to your finger if you poke it. At this stage, it is better not to add too much flour as this will result in dry buns. You can always add more later.
Once done, leave the dough in a bowl and cover with a tea towel or cling film. Allow to prove for around 30 minutes until it has doubled in size.
Dust your table top with flour and turn out the dough. Using your hands, knead the dough and work in more flour if needed. Cut the dough into 10 equal sized pieces.
Roll each piece of dough into a neat ball and place on a lined baking tray. Press down each roll until quite flat. Take a cup or glass that is approx. 2 inches (5 cm) in the base and use this to make a firm indent and hole in each bun. Fill the holes with a good tablespoon of Crème Patisserie and leave to rise, under a teatowel, for another 25 minutes.
Turn the oven to 200C.
Pop the buns into the oven to bake, for around 10-12 minutes. Watch the buns as the bake: they can go dark very quickly and you may also move the buns around in the oven if they are not baking evenly. The final baking time depends on your oven and you may have to adjust timings.
When golden, remove from the oven and leave to cool under a slightly damp teatowel (this prevents the buns from forming a crust). When cooled, make the icing: Mix hot water, drop by drop, with the icing until you have a smooth paste – the consistency like a thick syrup. Use a pastry brush to brush the sides of the buns with icing and immediately dust with the desiccated coconut before it dries.