Place milk and the bread flour in a small saucepan. Whisk until there is no more lumps. Cook this mixture over medium heat until it is thickened, about 5 minutes or less. Remove from the heat and let it cool down completely
Mix all the dry ingredients together in a mixing bowl. Make a well in the center and pour in the wet ingredients and the tang zhong you made earlier. Use a dough hook attachment to knead the dough until all the crumbly dough starts to come together into one mass, it may take about 2-3 minutes for this to happen. Don't be tempeted to add any liquid. You may need to stop halfway and scrap the dough off the hook and the sides of the bowl and knead again several times
Once it comes into a dough, stop the machine. The dough will not be smooth, don't worry.Cover the dough and let it rest for 20 minutes. This is an important rest that bakers refer to as an autolyse (though in our case it's a short one. Read my post above for detail)
After the rest, turn on and knead the dough again and knead for 1-2 minutes until it is a bit smoother. Then add the salt and sugar into the dough. Continue to knead until the dough is relatively smooth. You need to stop and scrape the dough off the hook and the bowl several times during this process. I promise it's worth the effort!
Once you have a smooth dough, turn the machine back on again to knead and gradually add in the softened butter a bit by a bit. The dough will turn into a REAL sticky mess again because of the butter, just keep kneading and stop halfway and scrape the dough off the hook and bowl again and continue to knead until the butter is absorbed by the dough. IT WILL HAPPEN, don't worry! DO NOTbe tempted to add any extra flour. You will get a shiny smooth dough that is very elastic. I promise!
Place this dough in a lightly oiled large bowl, cover it with a clean and damp tea cloth or plastic wrap and let it rise at a warm place for about 1 hour. It may not double in size, but it will puff up some for sure.
Line your baking sheet with a parchment paper. Punch the dough down and divide the dough into 10 smaller doughs. Cover these doughs loosely with a plastic wrap and let them rest for 15 minutes. Make sure you don't skip this part of resing the dough before shaping
Roll each ball out into a long rod shape, about 7-8 inches long. Wrap the hot dog with the rod and tuck the end at the bottom and place on a baking sheet. Repeat with the rest. Keep them covered while you are shaping the rest
Let the shaped dough proof again for another 40 minutes or until they are almost double in size again. Mix the egg with milk. Brush the top of the dough with egg wash
Preheat oven to 350 F and pop it into the oven (3rd rack from the top) and let them bake in the preheated oven for 15 minutes or until golden brown. Move them to the cooling rack to let them cool down
Tangzhong Chinese Sausage Buns (Hong Kong Style) https://whattocooktoday.com/tangzhong-chinese-sausage-buns-hong-kong-style.html