Begin by warming infusing your vanilla into your milk as you warm this to 104°F (40C). Place the milk in a small saucepan. Slice the vanilla pod in half lengthwise and scrape the vanilla seeds out. Add these along with the pod to your milk. Heat this until simmering over a medium-low heat. Once warmed, remove the pod and check that your milk is around 104°F (up to about 118°F is also fine). (see note)
Sprinkle the yeast and 1 teaspoon of sugar into the warmed vanilla milk, stir and set aside for 10 minutes until the yeast is foamy.
In the bowl of a stand mixer fitted with a dough hook, add your flour, bread flour, remaining sugar and salt. Give this a stir.
When the yeast is ready, add this to the flour mixture, immediately followed by two eggs and one egg white, reserving an egg yolk for an egg wash later. Knead on a low setting for 15 minutes until the dough is beginning to pull itself from the sides of the bowl. (see note)
Add the butter, bit by bit, continuing to knead on a low setting. Once all of the butter in incorporated, continue kneading for a further 15 minutes until the dough is again beginning to pull itself from the sides of the bowl.
Scrape the dough into a greased bowl, cover with plastic wrap and place in the refrigerator to proof for 8 hours (or overnight).