Preheat the oven to 350 degrees.
In a large bowl, cream together the oil and sugar until light and fluffy. Add the applesauce and milk and mix gently, it might make the oil clump and firm up a bit but that’s ok. Mix in the vanilla.
Add one cup of the flour, all of the cocoa powder, the baking soda and salt and mix well. Mix in the chocolate peppermint chunks and then add the final cup of flour and mix until it firms up. You might need to use gloved hands to get it fully incorporated.
Lightly grease baking sheets. Place a dozen on a baking sheet in 1 1/2 tablespoon scoops. Flatten slightly. Place a pinch of crushed candy cane in the center of each and press gently into the surface.
Bake for 10 minutes. Remove from oven and let cool for 5 minutes, then transfer to wire rack to cool completely.