Step 1

Make the filling: In a medium bowl, whisk together the egg yolks and sugar until smooth and pale yellow. Sift the cornstarch and cake flour into the bowl and whisk again until well combined. Add the milk and whisk until thoroughly combined.

Step 2

In a medium skillet over medium heat, melt the butter. Add the egg yolk mixture and stir constantly with a heatproof spatula until the mixture begins to solidify into a paste resembling a very wet dough, 5 to 7 minutes. Don’t be concerned if it starts to curdle — that’s normal. Transfer the custard to a glass container, smooth the surface and press a layer of parchment paper on the surface. Cover and refrigerate until cool, at least 1 hour and up to overnight.

Step 3

Make the mochi: Line a large, rimmed baking sheet with parchment paper and lightly sprinkle with an even layer of cornstarch or potato starch.

Step 4

In a medium bowl, whisk together the sweet rice flour, water, sugar and oil until it’s smooth and without any visible lumps.

Step 5

In a medium nonstick skillet over medium heat, add the batter and stir with a heatproof spatula until it forms a soft, pliable ball, 5 to 7 minutes. (Alternatively, you can microwave the batter in 1-minute increments for up to 3 minutes, stirring each time until it becomes soft and pliable.) Using well-oiled gloves or hands, transfer the dough to the baking sheet and divide into 20 (about 15-gram) pieces. Remove the custard from the refrigerator and divide it into 20 (22-gram) pieces.

Step 6

Dust another piece of parchment paper with cornstarch or potato starch and place a piece of dough on top. Dust lightly with more starch and cover with another piece of parchment. Using a rolling pin, roll out the dough to a 3-inch circle. Add a piece of custard to the center of the mochi and fold the mochi over the filling to enclose it.

Step 7

Lightly dust the inside of the mooncake mold with cornstarch or potato starch, then place the mochi in the mold. Flip the mold over and gently press down on an even, powdered surface for 10 seconds. Transfer to a serving platter and serve immediately or, to serve cold, transfer to a container with a lid and refrigerate for 30 minutes.

Step 8

NOTES: Mochi dough can become quite sticky, so there’s no shame in using extra oil to make molding easier. To brush off any extra cornstarch on the mochi, use a fluffy, clean paintbrush.For a vegan option, add red bean paste or mung bean paste to the center of the snow skin mochi; they're available online or at Asian markets.