Preheat oven to 350°F. Line three 6-inch round cake pans with parchment paper. Lightly grease and set aside.
In a large bowl, whisk together flour, cocoa powder, espresso powder, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat together oil, sugar, eggs, and vanilla until well combined.
On low speed, alternate adding dry flour mixture and milk. Add about 1/3 of flour mixture. Mix on low speed until almost incorporated. Follow with half of milk. Mix on low. Repeat adding another 1/3 of flour and remaining half of milk. Scrape down bowl as needed to ensure thorough mixing. Add sour cream and remaining 1/3 flour. Mix on low speed until there are no longer any streaks of dry flour.
Divide batter among prepared cake pans (about 370 g per cake pan). Level batter. Bake for 25-28 minutes until toothpick inserted in center of cake comes out clean. Rotate cakes midway through baking.
Allow cake to cool in pan for 5 minutes before unmolding. Run mini offset spatula around perimeter of cake to loosen from pan, if necessary. Let cakes cool to room temperature on wire rack.