01 - Combine bread flour, matcha powder, sugar, yeast, and salt in a large bowl. Mix thoroughly to distribute the matcha evenly throughout the flour.
02 - Pour lukewarm milk and crack the egg into the dry mixture. Stir with a wooden spoon until a shaggy, sticky dough begins to form and all flour is incorporated.
03 - Work softened butter into the dough, then knead until smooth and elastic—approximately 10 minutes by hand on a lightly floured surface or 6 minutes using a stand mixer with a dough hook. The dough should pass the windowpane test when stretched.
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 bubbles. Divide into 12 equal portions and roll each into a smooth ball, pulling the surface taut underneath.
06 - Flatten each ball into a 4-inch disc. Place a heaping tablespoon of red bean paste in the center. Gather edges upward and pinch tightly to seal completely, ensuring the filling is fully enclosed. Place seam-side down on a parchment-lined baking sheet.
07 - Cover the buns loosely with plastic wrap or a light towel. Let rise again until puffy and visibly expanded, about 40 minutes.
08 - Preheat oven to 350°F while buns complete their final rise.
09 - Whisk egg yolk with 1 tablespoon milk until smooth. Brush the tops of each bun gently with the egg wash using a pastry brush. 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. Rotate the baking sheet halfway through for even browning.
11 - Transfer buns to a wire rack and cool for at least 15 minutes before serving. Warm buns offer the best texture and flavor experience.