Make Tangzhong by mixing milk and flour in a microwave safe container. Microwave on high for 1 minute, mix.
Microwave on high for 1 minute, mix.
Microwave on High for 15 seconds, mix. Should thicken and become paste-like. If too thin, microwave for additional 15 second periods until thickened.
Warm the milk slightly... to about 100 F. Combine the milk, sugar, salt and eggs in a large pitcher. Mix with a stick blender until salt and sugar are well dissolved and eggs are mixed in.
Place egg mixture and Tanzhong into the mixer. Add the flour and yeast. Mix on low until somewhat uniform texture. Raise speed to 2nd and mix for about 5 minutes or until gluten is developed. Add butter while mixer is running, a little at a time. Let butter incorporate between each addition. When all butter is added and well incorporated, let dough mix for another 2 minutes.
Turn dough out onto the table, pat out and fold a few times. Place in a plastic container with a lid. Allow to rise until doubled in bulk. Turn back out onto the table and portion. Should make about 6 loaves (@ 545 grams each) or 48 rolls. Shape and allow to rise until doubled, about an hour.
While dough rises, preheat oven to 350F. Make the egg wash by beating the egg with the milk. A little sugar can be added to the egg wash if you want an even shinier result. Strain the egg wash to remove any clumps that wouldn't look good on the finished product.
When product has risen sufficiently, brush with egg wash and bake. You're looking for an internal temperature of about 200 F, or a tad less. If tops are getting too brown, cover with aluminum foil.
Turn out finished product onto a wire rack to cool.