In the bowl of a stand mixer fitted with the dough hook attachment, add ingredients in the following order: heavy cream, milk, egg, sugar, cake flour, bread flour, yeast, and salt. Turn the mixer on to the lowest setting to bring the dough together. Knead on low speed for 15 minutes. If needed, turn off the mixer to bring the dough together with a rubber spatula.
The dough should not stick to the sides of the mixer, but it may look a little bit sticky (sticking to the bottom of the mixer is ok). If you’re in a humid climate, and the dough is sticking to the sides of the mixing bowl, add more flour 1 tablespoon at a time until it comes together. Alternatively, you can stir all the dough ingredients together with a wooden spoon in a large mixing bowl, and then knead by hand for 20 minutes.
Shape the dough into a ball, and cover the bowl with an overturned plate or damp towel. Place in a warm spot to proof for 75-90 minutes, or until the dough doubles in size. (A good proofing environment is a closed microwave, with a mug of hot boiled water next to the bowl.)
While that's happening, mix the filling. In a medium bowl, combine the coconut, milk powder, sugar, salt, melted butter, egg yolks, and milk. Set aside.
After the first proof, knead for another 5 minutes to punch the air out of it. Then dump the dough on a lightly floured surface, shape it into a ball, and cut it in half. Cut each half of dough into 6 pieces, so you get 12 equal pieces of dough.
To shape the buns, knead and roll piece of dough into an even ball, and flatten. Roll into a 5x10 inch rectangle. Spread a layer of filling onto the rectangle, pressing the filling into the dough and leaving about a half inch of margin all around.
Roll the dough lengthwise into a cigar. Cut the cigar in half lengthwise, leaving it attached at the top end, so it looks like a long pair of pants. Twist the two pieces together, and then roll into a round spiral/snail shape, tucking the ends underneath the bun. Place onto a parchment-lined baking sheet. You’ll need two baking sheets, with 6 buns on each.
Cover with a damp towel, and proof the buns for 1 hour. Meanwhile, preheat the oven to 350 degrees, and position a rack in the middle of the oven.
Brush the risen buns with beaten egg, and bake for 22-26 minutes, until golden. Remove from the oven, and while the buns are still warm, brush with sugar solution.
If you don't have cake flour and/or bread flour, feel free to substitute all purpose flour for both.Though this recipe calls for active dry yeast, all the dough ingredients are combined in an all-in-one method, including the yeast. There is no need to activate the yeast in warm water beforehand. Make sure your yeast is within its expiration date!These buns are best enjoyed fresh and warm out of the oven. However, you can continue to enjoy them for 4-5 days. Store these buns in an airtight container on the counter for 1-2 days, and then store in the refrigerator. Microwave for 30 seconds to soften/warm them up before enjoying.