01 - Combine bread flour, matcha powder, sugar, yeast, and salt in a large bowl. Mix thoroughly until evenly distributed.
02 - Pour lukewarm milk and add egg to the dry ingredients. Mix until a shaggy, rough dough begins to form.
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 using a stand mixer with dough hook.
04 - Shape dough into a ball and place in a lightly greased bowl. Cover with plastic wrap or damp towel and let rise in a warm, draft-free area until doubled in size, about 1 hour.
05 - Punch down the risen dough to release air. Divide into 12 equal portions and shape each into a smooth ball.
06 - Flatten each dough ball into a disc. Place approximately 1 tablespoon of red bean paste in the center. Gather edges together and pinch firmly to seal completely. Place seam-side down on a parchment-lined baking sheet.
07 - Cover buns loosely with plastic wrap or towel. Let rise until noticeably puffy and expanded, about 40 minutes.
08 - Heat oven to 350°F.
09 - Whisk egg yolk with 1 tablespoon milk until combined. Brush the tops of each bun gently with the egg wash. Sprinkle with sesame seeds if desired.
10 - Place baking sheet in preheated oven. Bake for 18 to 20 minutes until buns are lightly golden and sound hollow when tapped on the bottom.
11 - Transfer buns to a wire rack. Cool for at least 10 minutes before serving warm or at room temperature.