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Preheat oven to 350 degrees and grease 3 round 9" cake pans well.
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Mix cocoa with hot coffee, stirring until cocoa is dissolved (the mix will be thick). Set aside to cool.
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With a mixer, beat butter and oil together until well combined, about 1-2 minutes. Add in both brown and white sugar 1/2 cup at a time, mixing after each addition.
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Once combined, add eggs one at a time, beating after each addition.
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Add in coffee/cocoa mixture and mix well.
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In a separate bowl, sift together flour, corn starch, baking soda, baking powder, salt, and espresso powder. Set aside.
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Stir milk, sour cream, and vanilla extract together.
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With the mixer on low, alternately add flour mixture and milk mixture to the chocolate batter, beginning and ending with flour mixture.
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Mix the batter until just combined, then disperse batter evenly between 3 cake pans.
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Bake for 25-30 minutes, or until a cake tester comes out clean. Allow cakes to cool completely before removing from pans.