Preheat oven to 350°F. Butter two 6-inch cake pans and line bottom with parchment paper. Set aside.
Sift together cake flour, cocoa powder, espresso powder, baking powder, baking soda and sea salt. Set aside.
In the bowl of a stand mixer fitted with paddle attachment, beat butter on medium speed. Slowly add sugar. Continue to mix, scraping down bowl as needed to ensure throughout creaming. Add eggs one at time, mixing on low speed. Add egg white and vanilla extract.
Add ⅓ of dry flour mixture and mix on low speed. Add ½ of buttermilk and mix until incorporated. Follow with another ⅓ of flour, then remaining buttermilk. Finish with last ⅓ of flour mixture. Mix on low speed until there are no longer any dry streaks of flour.
Divide batter evenly between the two prepared cake pans. Bake for 40-45 minutes until toothpick inserted in center of cake comes out clean. Let cool in pan for 5 minutes. Unmold the cake and set on a wire rack to cool to room temperature.