In the bowl of your stand mixer, combine water, levain, eggs, and honey. Add flour to the bowl, turn the mixer on, and mix for about 2 minutes until the dough comes together. You want to use the dough hook attachment for this. Cover the bowl and autolyse/rest for 30 minutes.
185 g water, 100 g levain, 40 g honey, 100 g eggs, 500 g bread flour
Turn the mixer on again and add the salt and 1/4 of the oil. Knead for 2 minutes or until the oil is thoroughly mixed in. Then, add another part of the oil and knead on low-medium speed until fully incorporated. Repeat until all the oil has been added. This dough is on the stiffer side, so depending on your mixer, you might have to squeeze the dough with your hands a little to thoroughly mix in the oil. Be patient with this part. The key is to add a little oil at a time.
10 g salt, 40 g neutral oil
Once you have added all the oil, knead for 5-10 minutes on low-medium until the dough passes the windowpane test.
Oil a large baking bowl. Transfer the dough to the bowl, and lightly oil the top of the dough as well. Cover the bowl and rise for five hours at around 75°F/24°C.
Transfer the dough to the fridge and cold-proof for 10-15 hours or overnight.