Preheat the oven to 350°F. Place the first six ingredients in a mixing bowl and whisk to combine. Mix in the chocolate chips or chopped chocolate. Place the eggs in second bowl and beat until blended. Whisk in the milk and vanilla.
Mix the dry ingredients into the wet until just combined. Now mix in the vinegar and butter.
Grease three, 12-cup, non-stick mini muffin pans with vegetable oil spray. Divide and spoon the batter into the prepared pans; filling each cup about 3/4 full.
Bake the cupcakes 18 to 20 minutes, or until they spring back in the very centre when gently touched. Let cupcakes cool in the pans 20 minutes, and then very carefully remove and set on a rack to cool. Finish cupcakes as described below.
To ice and to finish:
Place butter in a bowl, or bowl of your stand mixer. Sift icing sugar and cocoa into the bowl. Add the milk and beat until well combined and lightened. Pipe or spread the icing on the cupcakes. If desired, decorate each cupcake with a walnut half and enjoy.