In a large bowl, or the bowl of a stand mixer, combine the softened butter and both sugar until fully combined. Add in the egg and peppermint and again, mix to combine.
Add the flour, cocoa powder and baking soda and mix again using electric mixer. It might be a little stiff and sticky - if it's too stiff to work, add a tablespoon of milk.
Place dough in a bowl and cover, let chill 2 hours.
Pre-heat the oven to 355f/180c. Line two large baking trays.
Take the dough from the fridge, and roll into balls - I use a tablespoon to scoop, which creates about 12-14 cookies. Place the balls onto the trays, spaced apart (I do 6 per large tray).
Bake for 10-12 minutes. Remove from the oven, and place a marshmallow half on each cookie. Press down a little, then return to the oven for 3 minutes.
Remove and let cool.
Whilst cooling, crush your candy canes/peppermint candies. You can either use a rolling pin in a large bowl, or bash them while they are still in the packaging (much cleaner). Finally, you can use a knife to cut them, just take really good care as the super hard candies are difficult to cut so there's a risk of the knife slipping. Set aside the crushed candies in a bowl.
Once cool, melt the dark chocolate with the oil - In a small bowl, break up the dark chocolate, peppermint extract and oil and melt in the microwave in 20 second intervals, stirring in between to make sure it doesn't burn. Alternatively, set up a double boiler. Do this by placing a heatproof bowl over a small pot of simmering water. Add the chocolate, peppermint extract and oil to the heatproof bowl and stir until melted.
Spoon the melted chocolate over the marshmallows, so that the marshmallows are no longer visible.
Sprinkle over the crushed candy canes and leave to set.