Combine the warm milk, sugar, and yeast. Let stand for 5–10 minutes until foamy.
In the bowl of a stand mixer fitted with the dough hook, combine the bread flour, all-purpose flour, and salt.
Add the yeast mixture and cold water. Mix until a shaggy dough forms.
Add the softened butter and knead for 6–8 minutes until smooth and elastic.
Place the dough in a lightly greased bowl, cover, and let rise for 1 hour.
Shape into an 8 x 10-inch rectangle, wrap tightly, and refrigerate for 1–2 hours or overnight.