Preheat the oven to 350 degrees F. Grease two 8 1/2-9 inch cake pans.
Cream the butter & sugar together until pale and fluffy. Gradually add the eggs and peppermint extract to the creamed butter and sugar and mix until well incorporated.
Sift the flour, cocoa and baking powder together. Fold into the butter mixture. Add a splash of milk to loosen the mixture if it's too stiff.
Divide the mixture between the two prepared pans. Smooth over the surface so it's level. Bake for 25-30 minutes (Cake should be springy to touch and shrunk from the sides of the tin). Cool in pans for 10 minutes, then transfer to a wire rack to cool completely.
Once completley cooled, sandwich together with the whipped cream and crushed candy canes.