Preheat the oven to 350°F (180°C) and line two baking sheets with parchment paper. Set aside.
To the bowl of your stand mixer, add vegan butter and white and brown sugar and cream together.
Add peppermint extract and beat in.
In a separate bowl, sift the all-purpose flour and cocoa powder and then mix in the baking soda and salt. Mix together until combined.
Pour the dry ingredients into the wet and mix in by hand until crumbly.
Add the soy milk or other non-dairy milk and mix it into a thick cookie dough.
Add the chocolate chips and fold them in.
Roll the dough into balls and space them evenly over two parchment-lined baking sheets. Aim to get 20 cookies from the batch, 10 cookies per baking sheet.
Bake for 10 minutes. If the cookies are still very puffy when they come out of the oven, then you can gently flatten them with a fork while they are still soft and warm.
Allow to cool and firm up directly on the tray.
When the cookies have cooled down completely, prepare the topping. Add the chocolate and coconut oil to a microwave-safe bowl. Microwave in 30-second intervals bringing it out to stir every 30 seconds until melted and smooth.
Add peppermint extract and mix in until smooth.
Dip the cookies in the melted chocolate and place them back onto the parchment-lined baking sheet. Sprinkle crushed candy canes onto the melted chocolate.
Place the trays in the fridge for 5 minutes to set.