Step 1

To make the topping : In a large bowl or bowl of a stand mixer, beat together the butter and sugar until smooth, about 1 to 2 minutes.

Step 2

, Add the egg yolk and milk, then mix until smooth. Add the flour, milk powder, baking soda, baking powder, and salt. Mix until thoroughly combined. If the dough seems dry, add more milk a teaspoon at a time.

Step 3

, Form the dough into a log about 6" long and 1 1/2" wide and wrap tightly in parchment or plastic wrap. Refrigerate until ready to use.

Step 4

, To make the custard : In a medium bowl, whisk together the egg yolks, sugar, flour, cornstarch, salt, and 2 tablespoons (28g) of the milk.

Step 5

, In a medium saucepan, combine the remainder of the milk and the butter and bring to a simmer over medium-low heat.

Step 6

, Once the milk mixture is simmering, slowly whisk some of the hot milk mixture into the egg mixture, whisking constantly to temper it.

Step 7

, Pour the egg mixture back into the simmering milk through a strainer, which will help prevent lumps later. Continue to whisk constantly over medium-low heat until the mixture is thick and pudding-like, about 3 to 4 minutes. When you lift the whisk from the pan, the mixture should not be runny.

Step 8

, Remove from heat, whisk in the vanilla, and transfer to a bowl to cool. (If the custard is lumpy, pass it through a strainer a second time.) Cover and refrigerate until ready to use.

Step 9

, To make the tangzhong : Combine all of the ingredients in a small saucepan and whisk until no lumps remain.

Step 10

, Place the saucepan over low heat and cook the mixture, whisking constantly, until thick and the whisk leaves lines on the bottom of the pan, about 3 to 5 minutes.

Step 13

, Transfer the tangzhong to a large bowl or the bowl of a stand mixer.

Step 14

, To make the dough : Pour the cold milk over the tangzhong to help it cool to lukewarm.

Step 15

, Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Add the flour and remaining dough ingredients to the bowl with the tangzhong, then mix and knead — by mixer or bread machine — until a smooth, elastic dough forms; this could take almost 15 minutes in a stand mixer.

Step 16

, Shape the dough into a ball, and let it rest in a lightly greased bowl, covered, for 60 to 90 minutes, until puffy but not necessarily doubled in bulk.

Step 17

, Lightly grease two baking sheets, or line with parchment. On a lightly floured surface, gently deflate the dough and divide it into 12 equal pieces, about 55g each.

Step 18

, Shape each piece into a ball and place onto the prepared pan. You will be able to fit 6 buns per pan.

Step 19

, Cover buns and allow to rise for 40 to 50 minutes, until puffy.

Step 20

, Towards the end of the rising time, preheat the oven to 350°F and remove the log of cookie topping from the refrigerator. Allow the topping to rest on the counter for 10 to 15 minutes to make it easier to handle.

Step 21

, Slice the log into 12 equal pieces, about 31g each or roughly 1/2" wide. Place a piece between two small parchment squares and flatten with your palm until a 2 1/2" disc forms. You can also use a rolling pin to form the circle for a more precise cookie top, but it doesn’t have to be perfect.

Step 22

, Brush the top of each bun with the beaten egg yolk — just a dab in the center will do. (Brushing the entire surface will cause the cookie topping to shift during baking.) Drape each cookie topping over the bun (it won't cover the entire surface) and gently press down to secure it.

Step 23

, Brush the cookie topping with the beaten egg yolk and bake for 18 to 22 minutes, until the topping is golden brown and crackly.

Step 24

, Remove from the pans from oven and transfer them to a rack to cool. If filling with custard, allow the buns to cool completely.

Step 25

, To fill the pineapple buns : Transfer the cooled custard to a piping bag fitted with a small round tip or a plastic bag with the corner snipped off. Use a paring knife or chopstick to poke a hole in the middle of the bottom of the bun that’s large enough to fit the tip (or the end of your bag) and about 1" deep. Fill each bun with about 2 tablespoons of filling. Serve immediately.

Step 26

, Storage information : Store leftover pineapple buns, well wrapped and un-filled, at cool room temperature for 5 to 7 days; freeze for longer storage. If you plan to make these ahead, store the custard and the buns separately and fill the buns on the day you’ll serve them.