Preheat the oven to 350 degrees Fahrenheit. Grease two doughnut pans.

Stir flour, sugar, cocoa powder, baking soda, and salt in a mixing bowl. Add vanilla, egg, oil, coffee whitener, and food coloring and whisk until smooth. Transfer the batter to a piping bag or ziplock bag. Snip the corner to form a small hole and pipe the batter into the pans, until just about filled. Bake for 12-15 minutes (or three minutes in a preheated doughnut machine). Transfer to a cooling rack.

Mix frosting ingredients until smooth and drizzle over cooled doughnuts.