In a small bowl, add warm milk, warm water, and active dry yeast and mix. Set it aside for the yeast to bloom for 10 minutes or until creamy foam shows up on the surface. (This step is not necessary if using instant yeast. It can be added directly to the dry ingredients.)
In a large bowl, mix bread flour, granulated sugar, and salt.
Add the yeast mixture and ¾ beaten egg (40g to be exact) to the dry ingredients and mix. Set aside the leftover egg in a refrigerator.
Transfer the dough to the lightly floured work surface. Next, using your hand, knead by pushing the dough down and forward then folding the dough over itself. Repeat until it becomes smooth and elastic for about 10 minutes.This is a sticky dough but try not to add too much bread flour. If it is so wet that it coats your fingers when kneading, you can add a small amount of bread flour. A scraper can be a helpful tool to collect the dough. Spread the dough out on the work surface and add the softened butter. Then scrape the dough back into the center, and continue to knead the dough again until fully incorporated for about 5 minutes.
Place the dough ball in a bowl and cover with plastic wrap, and leave it at a warm place (about 90ºF/32ºC) for 1.5 hours or until doubled in size.
Make a fist with your hand and push the dough ball gently and firmly into the center and deflate it. Fold the edges of the dough into the center to form the deflated dough into a ball. Next, cover with plastic wrap and leave it again in a warm place for about 30-45 minutes.
Turn the dough onto a work surface. Divide the dough into 8 (about 50g each). Roll each dough into a small round shape. Place them one by one onto a baking sheet with parchment paper. Cover with plastic wrap loosely, let them rise for 1 hour in a warm place.
Preheat the oven to 450ºF/240ºC, and brush the dough balls with the leftover egg then bake for about 5-7 mins or until golden on top.
Once baked, let the buns cool completely.