Preheat oven to 350˚F. Grease baking pans with butter, or spray with cooking spray, then dust lightly with flour.
In 2 cup measuring cup, add vinegar then fill to the 2 cup line with milk. Stir. It will begin to look appear curdled, but that is ok. Set aside.
In a large stand mixer bowl, add boxed chocolate cake mix, flour, sugar, cocoa, espresso powder. Whisk to combine.
Add in the soured milk mixture, eggs, melted butter and vanilla. Mix on low until just incorporated, then scrape down the sides.
Mix on medium speed for 2 minutes, then divide evenly into prepared pans.
Bake for 25 minutes, or until toothpick inserted comes out clean.
Set on wire baking rack to cool completely.