01 - Combine bread flour, matcha powder, sugar, yeast, and salt in a large mixing bowl. Whisk thoroughly to ensure even distribution of matcha and yeast.
02 - Pour lukewarm milk into the dry mixture along with the room temperature egg. Mix with a wooden spoon or spatula until a shaggy, sticky dough forms.
03 - Incorporate softened butter into the dough and knead until fully absorbed. Continue kneading by hand for 10 minutes or use a stand mixer on medium speed for 6 minutes until the dough becomes smooth, elastic, and passes the windowpane test.
04 - Shape the dough into a smooth ball and place it 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, approximately 1 hour.
05 - Punch down the risen dough to release air pockets. Divide into 12 equal portions and roll each into a smooth ball.
06 - Flatten each dough ball into a 4-inch disc. Place approximately 1 tablespoon of red bean paste in the center. Gather the edges and pinch tightly to seal completely. Place seam-side down on a parchment-lined baking sheet.
07 - Cover the buns loosely with plastic wrap or a light towel. Allow to proof until puffy and noticeably expanded, about 40 minutes.
08 - Preheat the oven to 350°F while the buns complete their final rise.
09 - Whisk egg yolk with 1 tablespoon of milk until well combined. Gently brush the tops of each bun with the egg wash using a pastry brush. Sprinkle with sesame seeds if desired.
10 - Bake for 18 to 20 minutes until the buns develop a light golden-brown color 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. Serve warm or at room temperature.