Preheat oven to 350°F. Line three 6-inch cake rounds or two 8-inch cake rounds 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 (or using an electric hand mixer), 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 1/2 of milk. Mix on low speed. Repeat adding another 1/3 of flour and then remaining 1/2 of milk. Scrape down bowl as needed to ensure thorough mixing. Add sour cream and remaining 1/3 of flour. Mix on low speed until there are no longer any streaks of dry flour.
Divide batter among prepared cake pans. Level batter. Bake for 25-28 minutes until toothpick inserted in center of cake comes out clean. Rotate cakes midway through baking to ensure even cooking.
Allow cake to cool in pan for 5 minutes. Run mini offset spatula around perimeter of cake to loosen from pan. Unmold cake. Let cake layers cool to room temperature on wire rack.