Preheat the oven to 400 degrees. Grease a donut pan with baking spray and set aside.
In a bowl, mix flour, cocoa powder, brown sugar, granulated sugar, baking soda, salt, and espresso powder together until well combined. Set aside.
Whisk the egg, coffee, and half & half together. Make a well in the center of the dry ingredients, and add the wet ingredients. Mix until combined (batter will be fairly thick).
Add in sour cream, vanilla extract, and canola oil; mix until well combined.
Pour batter into greased donut pan, filling each donut cavity about 3/4 of the way full (this batter can make about 7-8 donuts).
Bake for 8-9 minutes, or until the donut 'springs' back when touched. Allow to cool a few minutes before removing from the pan.