Mix dry ingredients - Add the plain flour, sugar, salt, yeast and milk powder to the bowl of a stand mixer. Use the dough hook attachment to mix until combined. See notes if using a spiral mixer like the Ooni Halo.
Mix wet ingredients - In a large jug whisk together the eggs and milk until well combined.
First knead (15 min) - Add the wet ingredients and cooled tang zhong to the dry ingredients. Use the dough hook to mix the ingredients. Turn the mixer on 30% (that’s speed two on my Kenwood) and knead for 15 minutes.
Rest dough - Turn the mixer off and cover the bowl with plastic wrap. Rest the dough for 10-15 minutes. This will help relax the gluten in the dough and gives you an even smoother more elastic dough that is less sticky to work with later.
Second Knead - Knead the dough for 5 minutes on speed 2 (30% speed).
To test if dough is kneaded enough - Test by stretching a small piece between your fingers. It should form a thin, see-through sheet without tearing. Kneading time can vary depending on your mixer so focus on the dough’s feel rather than just time.
Add the butter and finish kneading - With the mixer on speed 2, add the softened butter a little at a time, letting each piece mostly mix in before adding the next. This will take about 5 minutes all up. Once all the butter is added, knead on medium low speed for about 5-10 minutes until the dough is smooth, elastic and comes away cleanly from the bowl. A slight stickiness at this stage is normal. If the dough begins looking overly shiny as the first bit of butter is added, it’s too warm. Cool the dough down in the fridge for 10 minutes before adding the remaining butter.
Room temp rise (Proof #1) - Add the dough to a large sized mixing bowl and cover with plastic wrap. Let it rise in a warm spot of the house for 1 hour or until doubled in size.
Cold rise (Proof #2) - Place the bowl of dough in the fridge for at least 2 hours, or up to 8 hours (overnight) for better flavor. The dough will continue to expand as it chills.
Your dough is ready! - Once the dough has finished chilling and doing its thing in the fridge it's ready for you to shape and bake. Baking time will depend on how you portion and shape it but the rule of thumb is to get it nice and golden on the outside. A loaf will generally take about 20-25 minutes and little buns will take about 12 minutes.