In a large mixing bowl, or the bowl of a stand mixer fitted with the dough hook attachment, combine the starter, water, milk, and granulated sugar. Stir by hand, spoon, or Danish dough hook until you form a slurry.
Next, add the flour and mix on low or by hand until you form a shaggy dough. Let fermentolyse (dough rest) for 30-45 minutes.
Start kneading the dough on low speed adding the salt and egg to the dough. Then add the butter one tablespoon at a time.
Knead the dough for 15-20 minutes until you have a strong gluten development, and the dough passes the windowpane test*. (See picture)
Once it has been kneaded transfer the dough to a medium bowl and cover with a bowl cover or plastic wrap.
Let rest on the counter for an hour before transferring the dough to the fridge to do a cold ferment for 5-8 hours or overnight.