In a small bowl, combine warm milk, sugar, and yeast. Let sit 5–10 minutes until foamy.
In a stand mixer bowl, combine bread flour, all-purpose flour, and salt.
Add yeast mixture and cold water. Mix until a shaggy dough forms.
Add softened butter and knead 6–8 minutes until smooth and slightly tacky.
Cover and let rest 1 hour until slightly puffy.
Shape dough into an 8x10-inch rectangle, wrap tightly, and refrigerate 1–2 hours.