01 - Combine bread flour, matcha powder, sugar, yeast, and salt in a large bowl. Mix thoroughly until evenly distributed.
02 - Pour lukewarm milk and crack the egg into the dry mixture. Stir with a wooden spoon or spatula until a shaggy, sticky dough forms.
03 - Incorporate softened butter into the dough and knead until fully absorbed and the dough becomes smooth and elastic, approximately 10 minutes by hand or 6 minutes using a stand mixer with dough hook attachment.
04 - Shape dough into a smooth ball and place in a lightly greased bowl. Cover with plastic wrap or a clean 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. Cover with a towel to prevent drying.
06 - Flatten each dough ball into a 3-inch disc. Place approximately 1 tablespoon of red bean paste in the center. Gather edges upward and pinch tightly to seal completely. Place seam-side down on a parchment-lined baking sheet.
07 - Loosely cover the formed buns with plastic wrap or a towel. Allow to rise until puffy and noticeably expanded, approximately 40 minutes.
08 - Preheat oven to 350°F during the final 15 minutes of the second rise.
09 - Whisk egg yolk with 1 tablespoon milk until combined. Gently brush the tops of each bun with the egg wash mixture. Sprinkle with sesame seeds if desired.
10 - 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 and let cool for at least 10 minutes before serving. Enjoy warm or at room temperature.