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Preheat oven to 350 degrees F. Place rack in lower third of oven. Spray two 9" round cake pans with a good coat of non-stick cooking spray.
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Sift together flour, both cocoa powders, baking powder, baking soda, and salt three times. Yes, THREE times to fully incorporate everything together; set aside.
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Whisk together yogurt and 1/4 cup lukewarm water; set aside.
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Whisk together eggs and vanilla; set aside.
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In a large mixing bowl, beat 2 sticks of butter on medium speed until light and fluffy. Turn mixer to low and stream in sugar. Beat until combined and smooth, about 2 minutes on medium-high speed. Turn mixer back to lower and stream in egg mixture. Mix until combined; scrape the sides of the bowl with a spatula, as needed.
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With the mixer on low speed, add 1/3 of the cocoa mixture to the batter, and beat until just combined. Add 1/2 of the yogurt mixture, and beat until just combine. Repeat with 1/3 cocoa mixture, remaining half of yogurt mixture, and last 1/3 of cocoa mixture; beat until just combined after each addition. Scrape the bowl with a spatula as needed.
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Divide the batter between the two prepared pans. Slam the pans on the counter top a couple times to remove bubbles and even batter.
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Bake 25 to 30 minutes or until a toothpick inserted in the center comes out clean. Remove cakes to a wire rack to cool completely. Remove from pans.