Whisk together flour, cocoa powder, baking soda, and salt. Set aside.
Beat eggs on medium speed with an electric mixer until frothy. Add sugar and mix well.
Whisk together milk, butter, and vanilla. Add half of milk mixture and half of flour mixture to the egg/sugar mixture. Mix until combined. Repeat with remaining milk mixture and flour mixture.
Preheat doughnut maker according to instructions. (If using a doughnut pan, preheat oven to 350*F and spray doughnut pan with nonstick spray. I didn't make mine this way, but I'd start out baking them for around 10 minutes and check.)
Transfer batter to a piping bag (or Ziploc bag with the corner snipped off) and pipe into doughnut maker. Bake until puffed and done. Let doughnuts cool completely on a wire rack.
**The number of doughnuts this recipe makes will depend on the size of your doughnut pan/doughnut maker. I ended up with *way* more doughnuts than I needed.