Gather all the ingredients. In the bowl of a stand mixer fitted with a dough hook, combine the bread flour, sugar, salt, cinnamon, nutmeg, cold milk, eggs, and sweet levain. Mix on medium speed until a dough forms. Cover the bowl and let it rest for 30 minutes.
Resume mixing on medium speed for about 10 minutes.
Gradually add the softened butter, one cube at a time, to the dough.
Once all the butter is incorporated, continue kneading on medium speed for 15-25 minutes, or until the dough passes the window-pane test.
Transfer the dough to a clean bowl and allow it to proof in a warm place (around 78°F/26°C) for two hours.
After the initial proof, move the dough to the fridge to cold-proof for at least six hours.