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 mixture. Stir until a shaggy, rough dough begins to come together.
03 - Incorporate softened butter into the dough and knead until fully absorbed and dough becomes smooth and elastic. This takes approximately 10 minutes by hand or 6 minutes with a stand mixer.
04 - Shape dough into a ball, place in a greased bowl, cover, and let rise in a warm area until doubled in size, about 1 hour.
05 - Punch down the risen dough. Divide into 12 equal portions and roll each into a smooth ball.
06 - Flatten each ball into a disc. Place approximately 1 tablespoon of red bean paste in the center. Gather edges together and pinch tightly to seal. Place seam side down on a parchment-lined baking sheet.
07 - Cover buns loosely with plastic wrap or towel. Let rise again until puffy and noticeably expanded, about 40 minutes.
08 - Preheat oven to 350°F during the final minutes of the second rise.
09 - Whisk egg yolk with 1 tablespoon milk until combined. Brush the tops of each bun with the mixture. Sprinkle with sesame seeds if using.
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 10 minutes before serving.