Using an electric hand mixer, beat butter, sugar and vanilla until pale and creamy. Add egg. Beat until well combined.
Sift flour, cornflour and cocoa powder over butter mixture. Add milk. Mix well. Divide in half. Press each half into a disc. Wrap each disc in baking paper. Refrigerate for 20 minutes.
Preheat oven to 160 degrees C. Line 2 baking trays with baking paper. Roll each disc out between 2 sheets of baking paper to 3mm thick.
Use a 12cm long tree-shaped biscuit cutter to cut 12 biscuits from each circle of dough. Place onto trays. Refrigerate for 15 minutes or until firm. Bake for 15 minutes or until firm to touch. Stand for 5 minutes. Transfer to a wire rack to cool.
Spread milk chocolate over flat side of each biscuit. Press 1 paddle pop stick onto 12 biscuits. Sandwich together with remaining biscuits. Refrigerate until firm.
Spoon white chocolate into a snap-lock bag. Snip off 1 corner. Pipe a zigzag pattern over trees. Decorate with M&Ms. Allow to set. Store in an airtight container.