Prep the glass: Spread a little honey or simple syrup on a small plate. Roll the rim of a chilled coupe or martini glass in it, then dip into crushed candy cane.
Set aside in the fridge while you mix the drink.
Melt the white chocolate: Place the white chocolate in a heatproof bowl and microwave in 10–15 second bursts, stirring until smooth. Let it cool for a minute so it doesn’t seize when mixed with cold ingredients.
Build the base: In a shaker, add vodka, white crème de cacao, peppermint schnapps, heavy cream, milk, and vanilla extract. Spoon in the melted white chocolate.
Shake hard with ice: Fill the shaker with ice and shake vigorously for 15–20 seconds.
You’re aiming for a frothy, well-chilled mixture that blends the chocolate evenly.
Strain and serve: Double strain into your prepared glass to catch any ice shards or chocolate bits. The drink should pour smooth and slightly thick.
Garnish: Add a mini candy cane on the rim or sprinkle on white chocolate shavings. Serve immediately.