Preheat oven to 350ºF. Line the bottom of two 6-inch cake pans with a circle of parchment paper. Rub a bit of butter around the inside walls of the pan, and lightly dust with some cocoa powder.
Whisk the flour, cocoa, baking soda, baking powder and salt together in a medium bowl; set aside.
Mix the milk, coffee and vanilla in a small bowl or measuring cup; set aside.
Add the butter and sugar to a medium bowl. Beat until creamy and well combined, about 3 minutes.
Add the egg to the creamed butter mixture, and beat until light and fluffy.
Add the flour and milk mixtures to the bowl. Mix on low until just combined, 15 to 30 seconds. Beat on medium-high speed for 15 seconds more.
Evenly divide batter between the prepared cake pans. Tap the pans on the counter to smooth the batter out in the pans. Bake 20 to 22 minutes, until a metal skewer inserted in the center comes out clean. Remove from oven and let rest on a cooling rack for 15 minutes. Tip the cakes from the pan by turning it upside down on the wire rack, leaving parchment circle intact, and let them finish cooling completely on the rack.
Once cooled, frost as desired.