Warm the milk to 43 C / 110 F in a small saucepan. Stir in the yeast and 1 tbsp of the sugar, let it sit for 5 to 10 minutes until foamy.

In the bowl of a stand mixer, combine the flour, remaining sugar, cardamom, and salt. Add the yeast mixture, egg, and softened butter.

Knead with the dough hook for 8 minutes until the dough is smooth and pulls away from the sides of the bowl.

Transfer the dough to a greased bowl, cover, and let rise for 45 minutes until doubled in size.

While the dough rises, whisk the egg yolks, sugar, and cornstarch together in a bowl until smooth.

Heat the milk in a 2-quart saucepan until steaming, then pour it slowly into the yolk mixture, whisking constantly.

Return everything to the saucepan and cook over medium heat, whisking, for 3 to 4 minutes until it thickens and coats the back of a spoon.

Off the heat, stir in the vanilla and a pinch of salt. Press plastic wrap directly onto the surface and chill until fully cool, at least 20 minutes.

Punch down the dough and divide it into 10 pieces, about 90 g each. Shape into smooth balls and place on a parchment-lined 13 x 18-inch sheet pan, spaced 2 inches apart.

Cover loosely and let proof for 30 minutes until puffy.

Press a deep indent, about 4 cm wide, into the center of each bun using your fingers or the back of a spoon.

Brush the edges of each bun with beaten egg. Spoon 1 to 2 tbsp of the cooled custard into each indent.

Bake at 190 C / 375 F for 14 to 16 minutes, until the dough is golden brown and the custard looks set but still glossy.

Cool the buns on the pan for 5 minutes, then transfer to a wire rack and let cool for 15 minutes more before glazing.

Whisk the powdered sugar with 2 to 3 tbsp milk until smooth and thick enough to coat a spoon.

Brush or drizzle the glaze over the cooled buns, avoiding the custard center.

Press the shredded coconut onto the wet glaze right away, before it starts to set. Serve once the glaze firms up, about 10 minutes.