In a bowl of a stand mixer fitted with a dough hook, combine the bread flour, milk, egg yolk, vanilla extract, salt & yeast. Withhold the butter.
Mix on slow speed for 2-3 minutes until all the dry ingredients are absorbed and a dough is formed.
Mix on high speed for 8-10 minutes or until the dough is smooth, shiny and very strong.
Once the dough is strong, turn the mixer back down to slow speed and add your butter. The butter will incorporate nicely if you pinch off marble-sized pieces and drop them in the mixer bowl while the mixer is running. Adding the butter should take about 5 minutes on slow speed.
Once the butter is incorporated, cover the dough in the bowl and let ferment at room temperature for 2 hours. The dough should grow during that time, but might not completely double in size.
Fold the dough by picking up each side and folding it over the middle of the dough. Refrigerate the brioche, covered, overnight.