In a shallow dish, combine the mochiko flour with water and give it a stir.
Cover with a lid and microwave for 1-2 minutes, stopping to stir the mixture after each minute.
Let the mochi cool slightly and divide into 10 equal portions. Keep the mochi covered.
Make the tangzhong:
Place the flour and milk into a small saucepan and heat over medium heat.
Whisk until it becomes thickened, about 2-3 minutes. The resulting consistency will resemble a thick gluey paste. Let it cool to room temperature.
Make the dough:
Next, add the cooled tangzhong to the rest of the dough ingredients in a stand mixer bowl fitted with a dough hook and knead until it becomes smooth. It shouldn’t be dry or sticky.
*Note: if using active dry yeast, bloom in lukewarm milk before adding to the flour.
Kneading the dough for long enough is important as this action produces gluten, which makes the dough smooth and elastic.
Transfer the dough to a lightly oiled bowl. Cover the dough and let it rest in a warm location, until doubled in size, about 1 hour, depending on how warm your environment is.
Fill the buns:
Divide the dough into 10 equal portions, and roll each portion into a ball.
Flatten the dough with a rolling pin.
Add a piece of mochi in the centre of the dough.
Next, add the red bean paste filling on top of the mochi piece, gather up the dough, and pinch the seams together.
Place the dough seam-side down on a baking tray lined with parchment paper.
Press the dough gently to flatten a little.
Repeat with the remainder and cover the buns with a cloth. Let the buns rise in a warm location until puffy and doubled in size.
Towards the end of the proofing time, preheat oven to 350°F/177°C.
Brush the tops of the buns with a little milk.
Bake the buns at 350°F/177°C for 18-20 minutes, or until lightly golden brown on top (if it's browning too quickly, cover with aluminum foil halfway).
Let the buns completely cool before adding in the whipped cream.
Make the whipped cream:
In a chilled bowl, combine the heavy cream with powdered sugar. Add in the vanilla extract and whisk until stiff peaks forms.
If making injeolmi whipped cream: add in 2 tablespoon of roasted soy bean powder (injeolmi) to the whipped cream.
Transfer the cream to a piping bag fitted with a long piping tip.
Assemble the buns:
Use a chopstick to poke a hole in the side of the cooled bun. (Aim for the upper third of the bun). Wiggle the chopstick a little to make cavity for the cream.
Pipe the whipped cream into the bun.
Smear about 1-2 tablespoons of whipped cream over the entire surface of the bun.
Put the injeolmi powder into a bowl or shallow dish.
Place the cream-covered bun into the bowl with the injeolmi powder and coat the entire bun with the powder.