Start by making your Tangzhong paste:

Put wheat flour and milk in a small saucepan and whisk them well and thoroughly together.

Turn on medium-high heat (9 out of 14 on my stove) and let it thicken while whisking occasionally.

It takes a bit of time, so be patient. When it boils, it thickens a lot, and you need to whisk thoroughly.

Turn off the heat and let it cool. For example, use a dough scraper to scrape it into a bowl, which you then place in the fridge.

When the paste is at room temperature (about 20 degrees Celsius (68 degrees Fahrenheit)), start making the dough.

Put the warm milk in a mixing bowl along with the yeast. Stir it together before adding sugar, salt, egg, and flour.

Put the paste in the bowl and turn on the mixer. Let it run for about 5 minutes on one of the lower settings.

Cut the butter into smaller pieces and add a few pieces at a time to the dough while the machine is still kneading - you might want to turn up the speed a bit now.

Now let the machine run until the dough releases from the sides - this can take anywhere from 15-20 minutes, so be patient.

If you have a good mixer, it can be done faster.

The dough is ready when it can pass the gluten test, i.e., you can take a lump of dough and stretch/pull it. Wet your hands with cold water before doing the test. It passes the test if you can stretch it far without it breaking.

Then put the dough onto a floured countertop.

Get out a baking scale and weigh balls of about 80 grams each.

Roll them into buns and place them on 2 baking trays lined with baking paper. I got 20 out of my portion.

Cover with clean dish towels and let rise for 1-2 hours.

Brush the buns with egg on top and bake them in the oven for about 15 minutes at 200 degrees Celsius (392 degrees Fahrenheit) conventional oven.

Knock on the bottom of the buns; they should sound hollow - then they are ready.

Let them cool on a rack - enjoy.