01 - In a large bowl, combine bread flour, matcha powder, sugar, yeast, and salt. Mix thoroughly to distribute the matcha evenly throughout the flour.
02 - Pour lukewarm milk into the dry mixture and crack in the egg. Stir with a wooden spoon until a shaggy, sticky dough forms.
03 - Work softened butter into the dough, kneading until fully incorporated. Continue kneading for approximately 10 minutes by hand or 6 minutes with a stand mixer until the dough becomes smooth, elastic, and passes the windowpane test.
04 - Shape dough into a smooth ball and place in a lightly greased bowl. Cover with plastic wrap or a damp towel 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 dough ball into a 4-inch disc. Place a heaping tablespoon of red bean paste in the center. Gather the edges around the filling and pinch tightly to seal. Place seam-side down on a parchment-lined baking sheet.
07 - Cover the buns loosely with plastic wrap or a clean towel. Let rise until puffy and noticeably larger, about 40 minutes.
08 - During the final rise, preheat your oven to 350°F.
09 - Whisk egg yolk with 1 tablespoon milk until combined. Brush the tops of the risen buns generously with the egg wash. Sprinkle with sesame seeds if desired.
10 - Bake for 18 to 20 minutes until buns are lightly golden on top and sound hollow when tapped on the bottom.
11 - Transfer buns to a wire rack and let cool for at least 15 minutes before serving. Warm buns offer the best texture and flavor experience.