Chop the chocolate into small pieces. Place in a microwave-safe bowl and microwave until nearly melted (it's okay if small chunks remain), stirring every 15-20 seconds.
Bring heavy cream to a simmer in a small saucepan. Stir in peppermint extract.
Pour heavy cream over chocolate and gently stir in one consistent direction, until the mixture is smooth and shiny (this is ganache).
Refrigerate ganache until it is firm but not solid, 1 to 3 hours.
Cover a small cutting board or sheet pan with parchment paper. Use a teaspoon to scoop the firm ganache into even balls and place on parchment (each ball should be about 1 1/2 teaspoons). Use your hands to gently form the balls, but you'll be able to perfect them in the next step.
Refrigerate for 20 minutes more, just to give the ganache balls time to firm up a bit more.
Using your hands, form the ganache into round balls and then roll in crushed candy canes, pressing the candy canes into the ganache. (This works great as a two-person task. One to roll the balls and one to coat in candy canes. The chocolate-roller will have very messy hands!)
Refrigerate for up to a week until ready to serve, but bring to room temperature before serving. These are best served at room temp. Enjoy!