Place the finely chopped chocolate and room temperature butter into a medium heat-proof glass or stainless steel bowl.
In a small saucepan, heat the heavy cream over medium-high heat until it reaches a gentle simmer (approximately 180°F/82°C), ensuring it does not reach a rolling boil.
Immediately pour the hot cream over the chocolate and butter mixture; let stand undisturbed for 5 minutes to allow for even heat distribution.
Using a rubber spatula, stir the mixture in small concentric circles starting from the center and moving outward until a smooth, emulsified ganache forms.
Incorporate the peppermint extract into the ganache and stir until fully combined.
Cover the surface of the ganache directly with plastic wrap to prevent a skin from forming and refrigerate for 2 hours or until firm enough to scoop.
Line a baking sheet with parchment paper.
Using a small scoop or teaspoon, portion the ganache into 15g rounds.
Quickly roll each portion between your palms to form a smooth sphere.
Toss half of the truffles in the crushed peppermint candies and the remaining half in the cocoa powder until evenly coated.
Return the truffles to the refrigerator for 15 minutes to set before serving.