Preheat oven to 325 degrees Fahrenheit (163 degrees Celsius) and line three 6 inch pans with parchment paper.
In a medium-sized bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or a medium-sized bowl if using a handheld mixer, beat the butter and oil together until combined and completely homogeneous - this will only happen if the butter is completely at room temperature. About 2-3 minutes on high speed.
With the mixer on low, slowly stream in the granulated sugar, then turn it up to medium-high speed and beat until light and fluffy. About 1 minute, scraping down the sides and bottom of the bowl as necessary.
Then, with the mixer on low, add the eggs in, one at a time, scraping down the sides and bottom of the bowl and mixing well in between each addition. Add the vanilla extract and mix on low until combined.
Add half of the dry ingredients and mix on low until just combined. Add half of the milk, half of the coffee and half of the yogurt and mix on low until just combined. Repeat this with the remaining halves of dry ingredients, milk, coffee and yogurt. Do not overmix!
Separate the batter equally between the prepared pans and spread it into an even layer. Bake the cakes for 40-43 minutes until a toothpick inserted into the center of the cake comes out clean. The cake will be slightly pulling away from the edges of the pan. Let the cake sit in the pan for 5-10 minutes, then remove them onto a cooling rack to cool completely.