Preheat oven to 350°F/175°C. Spray a donut pan with vegetable spray.
In a small bowl, prepare the flax egg and set it aside.
In a microwave-safe mixing bowl, add the vegan butter. Heat in a microwave until melted, around 20 seconds. Set aside.
Stir together the flour, cocoa powder, baking powder, baking soda, and nutmeg. Make a well in the center.
Add the sugar, milk, vinegar, flax egg, and food coloring. Stir to combine. (See notes for food coloring options).
Stir the liquid mixture and the flour mixture together until combined.
Use a spoon to evenly distribute the batter in each donut compartment, filling each to the top. This batter should fill up 6 compartments.
Bake 10 to 15 minutes, until the donuts are done and slightly golden colored on the top.
Remove from the oven and allow to cool for a couple of minutes.