Preheat the oven to 350°F / 175°C. Butter and line a 1.25 lb (9x5) loaf pan with parchment paper.
In a medium-sized bowl, whisk together the flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or with a hand mixer, beat together the butter, oil, and sugar for 5 minutes until light and fluffy.
Scrape down the sides of the bowl, and add in one egg at a time, beating until combined after the two additions.
Add in the egg white, vanilla, and sour cream and beat until combined.
Alternate between adding the flour mixture and the milk. Fold in ½ of the flour mixture, then all of the milk, followed by the rest of the flour mixture.
Brew the espresso. In a small bowl, whisk together 24g (¼ c.) of cocoa with 30g (1 oz.) of the espresso. In another small bowl, whisk together 6g (1 tbsp.) of cocoa with the remaining 1 oz. of espresso.
To the bowl with more cocoa, add in 1 c. of batter. To the bowl with less cocoa, add in 1 ⅓ c. of batter. Mix each bowl just until no streaks remain.
Alternate scooping in the three different batters into the loaf pan. Once all the batter has been used, use a knife to gently swirl the batters together.
Bake for 40-50 minutse, or until a knife inserted in the middle of the cake comes out with just a few moist crumbs.
While the cake is cooling, make the espresso ganache.