Begin by sprinkling the yeast and a teaspoon of the sugar into your warmed milk. Stir and set aside for about 10 minutes until the yeast has developed a foam on top.
Meanwhile in the bowl of a stand mixer fitted with a dough hook, add the flour, bread flour, remaining sugar and salt. Give this a quick stir.
Once the yeast is frothy, add this to the flour mixture, immediately followed by two full eggs and one egg white. Reserve the remaining egg yolk to make an egg wash later. (see note)
Turn the mixer to a low setting and knead for 15 minutes, stopping once or twice early on to scrape down the sides of the bowl to ensure all of the flour is incorporated. After 15 minutes your dough should have come together and be pulling itself from the sides of the bowl (though it will still be sticky).
With the mixer still on a low setting, slowly begin adding the butter a couple of bits at a time. Once all of the butter is incorporated, continue kneading for 15 minutes until the dough has come together again and is pulling itself away from the sides of the bowl. (see note)
Scrape the dough into a greased bowl, cover with plastic wrap and set in the refrigerator to proof slowly for about 8 hours (or overnight).