Butter or oil two cake pans (we used 9-inch cake pans) and line the bottoms with parchment paper by measuring out a square of parchment paper that fills the bottom, pressing it into the pan so you get the outline of a circle, and cutting out the circle. If you have pre-cut round sheets of parchment, you can use those!
Preheat the oven to 350 F (175 C).
Add your room temperature eggs and granulated sugar to the bowl of a stand mixer or a mixing bowl. Using your stand mixer, or a hand mixer, whisk together the sugar and eggs for about 5 minutes until the mixture is lightened considerably and has reached ribbon stage: when you lift the whisk out of the mixture, it should flow off the whisk and sit for a second or two on the surface of the mixture before sinking in.
Mix together coffee/espresso with milk in a small bowl/measuring cup. You can mix hot coffee and cold milk, and it will even out the temperature, but make sure the mixture is not too cold - heat it up in the microwave for short 5 second bursts if needed to get it closer to room temperature.
Add the vanilla extract and oil to the coffee/milk mixture and stir with a spoon to combine (it will not combine entirely - the oil will naturally separate).
Combine your dry ingredients (flour, cocoa powder, baking powder, and salt) in a separate bowl.
Now it's time to combine the ingredients for the batter. Add half of the wet ingredients to the mixer and run the mixer for just around 5-10 seconds.
Then, sift in half of the dry ingredients and do the same, running the mixer for 5-10 seconds. It's important to sift when using cocoa powder since it can be so lumpy!
Repeat with the rest of the wet, running the mixer for 5-10 seconds, then the rest of the dry, running the mixer for 5-10 seconds or until everything looks incorporated. Give the final mixture some folds with a rubber spatula to make sure it's well combined, but do not overmix!
Divide the mixture evenly between the two cake pans and place in the oven. To be completely accurate, you can weigh the batter into the pans.
Bake for 18-20 minutes, or until a cake tester comes out clean.
After you remove the cakes from the oven, let them cool for about 5 minutes. Then run a knife along the edge of the pans and remove the cakes from the pan, leaving them to cool on a wire rack. If you're doing this the day before assembly, wrap them in cling film and refrigerate until you're ready to assemble the cake layers. If you don't have room in the fridge, wrapping them and leaving them at room temp will also work just fine.