Prep the pan: Line the bottom of a 9-inch springform pan with parchment. Lightly grease the sides if you like cleaner release.
Make the crust: In a bowl, stir cookie crumbs, melted butter, sugar, and salt until the texture resembles wet sand.
Press the mixture firmly into the bottom (and slightly up the sides) of the pan. Use a flat-bottomed glass to compact it well. Chill while you make the filling.
Whip the cream: In a cold bowl, beat 1 cup heavy cream to stiff peaks.
Set aside. This will lighten the cheesecake without baking.
Blend the base: In a separate bowl, beat cream cheese until smooth and fluffy, about 2 minutes. Add powdered sugar and beat again until no lumps remain.
Mix in vanilla and peppermint extracts. Taste and adjust peppermint extract—start small; it’s strong.
Add white chocolate (optional): If using, fold in melted and cooled white chocolate. It adds body and a subtle sweetness.
Fold in whipped cream: Gently fold the whipped cream into the cream cheese mixture until just combined.
Avoid deflating it; you want a light texture.
Stir in peppermint crunch: Fold in the finely crushed peppermint candies. For a pretty pink marbled look, add a couple of drops of red gel food coloring and gently swirl without fully mixing.
Fill and smooth: Pour the filling over the chilled crust. Smooth the top with an offset spatula.
Tap the pan gently on the counter to release air bubbles.
Chill to set: Cover and refrigerate for at least 6 hours, ideally overnight. The longer chill helps it slice cleanly.
Make the topping: Whip the remaining 1 cup heavy cream with powdered sugar and vanilla to medium-stiff peaks. Spread or pipe over the set cheesecake.
Garnish: Sprinkle with crushed candy canes and, if you like, a handful of mini chocolate chips or chocolate shavings.
Slice and serve: Run a warm knife around the edge of the pan before releasing.
Wipe the knife between slices for neat edges.