In the bowl of your stand mixer fitted with a dough hook, combine bread flour, sugar, yeast, salt, eggs, and the initial amount of milk. Start with the lesser amount of milk and add more as needed to achieve a soft dough consistency. Mix on low speed until the dough starts to pull away from the sides of the bowl, approximately 10-15 minutes.
Gradually incorporate the softened butter, adding a few cubes at a time, and continue kneading on medium speed. The dough should be kneaded for another 10-15 minutes until it passes the window-pane test, indicating it’s properly kneaded.
Shape the dough into a smooth ball and place it in a lightly oiled bowl. Cover the bowl with plastic wrap or a clean kitchen towel.
Place the bowl in the refrigerator and allow the dough to chill for 10-18 hours, or overnight.