In a large bowl of an electric mixer, add the water, sourdough starter, milk, sugar, and oil. Mix by hand until it is combined.
Add the flour and mix either by hand or with the dough hook attachment on low for around a minute until you have a shaggy dough. Let stand covered with a tea towel for 30 minutes. (Fermentolyse)
After the 30 minutes, add the salt and eggs and knead on lowest setting on the stand mixer for 10 minutes, scrape the sides of the bowl as needed. Or once the eggs and salt are incorporated transfer to a lightly floured surface and knead by hand for 10 minutes.
Transfer to a medium bowl. Rest covered with a tea towel on the counter for 1 hour.
After the hour cover with plastic wrap and store in the fridge overnight.