Melt 2 tbsps butter in a non-stick saucepan over medium-low heat. Add condensed milk then add cocoa and peppermint extract, stirring constantly. After about 10 minutes, the mixture will thicken – you’ll see the bottom of the pan.
Use half of the remaining butter to coat a dinner plate. Pour the chocolate mixture onto it and spread evenly. Refrigerate for 30 minutes.
Wash your hands well then butter them with the remaining butter. Spoon about 1 tsp of the chocolate mixture into your hands and roll into a ball. Continue with the rest of the chocolate mixture.
In a small microwave-safe bowl, melt white chocolate uncovered at 50% power for 90 seconds and stir until smooth (if the chocolate isn’t quite melted, repeat for 15 second intervals).
Dip the chocolate balls into the white chocolate, fully covering them. Then dredge them in the candy canes.