Preheat the oven to 325 degrees and line an 8-inch square pan with parchment paper. Mix the chocolate cookie crumbs with the melted butter until evenly combined, then press the mixture firmly into the bottom of the pan.

Bake the crust for 8 minutes, then set it aside to cool while you prepare the filling. In a mixing bowl, beat the cream cheese and sugar until smooth.

Add the egg, vanilla extract, and peppermint extract to the cream cheese mixture and beat until fully blended. Pour the filling over the cooled crust and spread it evenly.

Bake for 20 minutes until the edges look set but the center still has a slight jiggle. Remove the pan from the oven and let it cool to room temperature.

Sprinkle the semisweet chocolate chips over the warm cheesecake layer and let them melt for a few minutes, then spread them gently with a spatula. Top with the crushed candy canes and chill the bars in the refrigerator for at least 2 hours before slicing.