Mix the warm milk, yeast, sugar, and whole egg in a large bowl.
Allow to sit for 6 minutes until frothy.
Add bread flour to the yeast mixture, mixing until well combined.
Incorporate the squid ink and salt, mixing until the dough is uniformly colored.
Transfer the dough to a baking mat and spread butter evenly over its surface. Knead for about 15 minutes, until smooth and non-sticky.
Cover the dough and let it rise in a warm area for 40 minutes, or until doubled in size.
Remove the dough from the bowl, knead it, and gently press it to let out some air.
Divide the dough into 8 equal parts.
Shape each into a smooth ball.
Place on a parchment-lined baking tray. Let them rise for an additional 10 minutes.
Preheat the oven to 392°F (200°C). Whisk together the egg yolk and milk for the egg wash. Brush the buns with the egg wash.
Sprinkle sesame seeds on top.
Place the tray in the oven.
Bake for 15 minutes, or until the buns are fully risen and have a crisp exterior.
Remove the buns from the oven and let cool on a rack before serving.