Line a 9-inch springform pan with parchment paper and lightly grease the sides.

Prepare the brownie batter as directed on the box, then pour it into the prepared pan. Bake at 350°F (175°C) until just set, about 20 minutes. Allow it to cool completely.

Beat the softened cream cheese until smooth. Gradually add the granulated sugar, blending well. Mix in the sour cream, melted chocolate, espresso powder, and peppermint extract. Add eggs one at a time, mixing on low speed until just incorporated.

Pour the cheesecake mixture over the cooled brownie crust. For even baking, place the pan in a larger dish and fill it with hot water halfway up the sides. Bake at 325°F (160°C) for 55-65 minutes.

Turn off the oven, crack the door, and let cheesecake sit for 1 hour, then cool completely at room temperature before refrigerating for at least 6 hours or overnight.

Heat heavy cream until steaming, pour over chopped dark chocolate, let sit for 1 minute, then stir until smooth. Spread ganache over cooled cheesecake and refrigerate until set.

Top with whipped cream and crushed peppermint candies just before serving.