Preheat the oven to 350 degrees F.
In a large mixing bowl, whisk together the cocoa powder, flour, baking powder, baking soda, salt, and brown sugar until combined.
In a small bowl, stir together the egg, milk, peppermint extract, vinegar, and ⅓ cup coconut oil until combined.
Add the egg mixture to the flour mixture until thoroughly combined.
Lightly spray a doughnut pan with non-stick cooking spray and spoon in the batter until the wells are ¾ full.
Place in the oven and bake for 12 to 15 minutes or until the doughnuts have set. Allow the doughnuts to cool in the pan 2 to 3 minutes before transferring to a wire rack to cool completely.
Using a double boiler, on medium-low heat, melt the chocolate chips and 2 tablespoons of coconut oil until smooth. Remove from the heat and dip the tops of the doughnuts and top with the crushed peppermint candy.
Allow the chocolate topping to set and enjoy.