The night before: In a large bowl, combine the flour, water, olive oil, sourdough, and 1/4 cup cocoa powder. Mix until very well combined and a sticky dough forms. Cover with plastic wrap and let sit on the counter overnight (up to 24 hours).
The next day: Preheat oven to 350F. Grease two 9" cake pans with butter and line the bottoms with parchment paper.
In the bowl of a stand mixer fitted with the whisk attachment, combine the sugar and eggs. Beat for 2 minutes, until light and fluffy.
Add the milk, sour cream, remaining 1/2 cup cocoa powder, baking soda, vanilla, salt, and espresso powder. Whisk until smooth.
Add the chocolate sourdough mixture and mix just until a smooth batter.
Divide the batter evenly between the two prepared cake pans.
Bake in the middle rack of the oven for 25-30 minutes, until centers are set and a toothpick inserted into the middle comes out clean.
Let cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.