01 - Combine bread flour, matcha powder, sugar, yeast, and salt in a large bowl. Mix thoroughly to distribute ingredients evenly.
02 - Pour lukewarm milk and cracked egg into the dry mixture. Stir until a shaggy, uneven dough begins to form.
03 - Work softened butter into the dough, kneading until fully incorporated and the texture becomes smooth and elastic—approximately 10 minutes by hand or 6 minutes with a stand mixer.
04 - Shape dough into a ball and transfer to a lightly greased bowl. Cover and place in a warm area to rise until doubled in volume, about 1 hour.
05 - Punch down the risen dough to release air. Divide into 12 equal portions and roll each into a smooth ball.
06 - Flatten each dough ball into a disc shape. Place a heaping tablespoon of red bean paste in the center, then gather and pinch the edges together to seal completely. Place seam-side down on a parchment-lined baking sheet.
07 - Cover the shaped buns loosely with a towel and allow to rise until puffy and expanded, approximately 40 minutes.
08 - Heat oven to 350°F.
09 - Whisk egg yolk with 1 tablespoon milk until blended. Brush the tops of each bun with the mixture and sprinkle with sesame seeds if using.
10 - Bake for 18 to 20 minutes until the buns develop a light golden color on top.
11 - Remove from oven and allow buns to cool briefly on the baking sheet before serving.