01 - In a large bowl, combine bread flour, matcha powder, sugar, yeast, and salt. Mix thoroughly to distribute evenly.
02 - Pour lukewarm milk and crack the egg into the dry ingredients. Mix until a shaggy, rough dough comes together.
03 - Work softened butter into the dough, kneading until fully incorporated and the dough becomes smooth and elastic—approximately 10 minutes by hand or 6 minutes with a stand mixer.
04 - Shape dough into a ball and place in a lightly greased bowl. Cover and let rise in a warm, draft-free area 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 ball into a disc. Place a heaping tablespoon of red bean paste in the center. Gather edges together and pinch firmly to seal, then place seam-side down on a parchment-lined baking sheet.
07 - Cover buns loosely with plastic wrap or kitchen towel. Let rise until puffy and noticeably expanded, approximately 40 minutes.
08 - Preheat oven to 350°F while buns complete their final rise.
09 - Whisk egg yolk with 1 tablespoon milk until blended. Brush the mixture generously over the tops of the risen buns. Sprinkle with sesame seeds if using.
10 - Transfer baking sheet to oven and bake for 18 to 20 minutes, rotating once halfway through, until buns are lightly golden and sound hollow when tapped.
11 - Remove from oven and let buns cool on the baking sheet for 10 minutes before serving warm or at room temperature.