Preheat oven to 350F, and line a baking sheet with parchment paper.
Using a mixer, cream together the butter and brown sugar until combined. Add the flax egg, vanilla extract and salt, and beat until well mixed.
One at a time, mix in the raw cacao, flour and baking soda, and mix until combined.
Scoop 1 tbsp of dough into your hands and roll it into a small 1-inch ball (I find it helps to have damp hands so the dough doesn't stick). Repeat until all of the dough has been rolled into balls. Press down and on each ball lightly so they make a round disk.
Bake for 10 mins on the middle rack, then remove from the oven and allow the cookies to cool on the baking sheet until they reach room temperature.
To make the buttercream, beat the chilled butter, powdered sugar and peppermint extract on medium speed until light and well combined. Add plant-based milk and peppermint extract, and mix until smooth.
Pipe approximately 1 tbsp of peppermint buttercream onto half of the cookies (or spread with a spoon). Then pop the other half of the cookies on top of the buttercream to create a sandwich.
Drizzle with melted white chocolate and sprinkle with crushed candy cane.
These cookies will last for up to 5 days in the fridge.