In a large mixing bowl, combine bread flour, cake flour, granulated sugar, salt or miso, and active dry yeast.

In a separate bowl, whisk together the warmed milk, egg, and softened butter.

Pour the wet ingredients into the dry ingredients and mix until just combined.

Cover the bowl with plastic wrap or a damp cloth and let it rest for about 1 hour, or until the dough has doubled in size.

Preheat the oven to 375°F (190°C).

Once the dough has risen, divide it into 9 equal portions and shape each portion into a bun.

Place the buns on a baking sheet lined with parchment paper.

Brush the tops of the buns with the beaten egg for an egg wash.

Bake in the preheated oven for 35 minutes, or until golden brown.

While the buns cool, prepare the frosting by mixing cream cheese, softened butter, miso, vanilla extract, Black Sesame Crunchy Butter, and confectioners’ sugar until smooth.

Frost the cooled buns and dust with black sesame powder if desired.