Preheat oven to 350 degrees F (175 degrees C).
Grease a 9-inch round cake tin with butter and line with parchment paper.
Add eggs and sugar to the bowl of a stand mixer or a mixing bowl. Beat eggs and granulated sugar together until light in color and doubled or tripled in size. Use a stand mixer with a whisk attachment, or an electric hand mixer – it will be more difficult to whisk by hand, but it can be done!
Add in vanilla extract and mix to combine.
Combine the dry ingredients in a bowl: flour, cocoa powder, baking powder, and salt.
Combine oil, coffee, and milk in a separate bowl or container.
Alternate mixing in the dry and wet ingredients to the batter, adding in half the ingredients each time. Be sure to sift in the dry ingredients to avoid lumps. Mix on low speed between additions.
Once the batter is combined, pour it into the lined cake tin.
Bake for 20-25 minutes, until a knife inserted in the center comes out clean. It can be hard to tell when chocolate cake is done, but try not to overbake or the cake may be dry!