Prep the pan and oven: Heat the oven to 325°F (163°C). Grease a 9-inch springform pan and line the bottom with parchment.
Wrap the exterior of the pan with a double layer of foil if your pan tends to leak; it helps prevent butter drips.
Make the crust: Stir cookie crumbs, melted butter, sugar, and salt until the texture resembles wet sand. Press firmly into the bottom of the pan and slightly up the sides. Bake for 8 minutes, then cool while you prepare the filling.
Melt the white chocolate: Combine chopped white chocolate and 1/2 cup heavy cream in a heatproof bowl.
Melt gently using a double boiler or in short microwave bursts (15-20 seconds), stirring between each until smooth. Set aside to cool until just lukewarm.
Beat the cream cheese: In a large bowl, beat cream cheese with sugar on medium speed until smooth and fluffy, about 2 minutes. Scrape the bowl.
Add sour cream and mix until combined.
Flavor it: Beat in vanilla, peppermint extract, and salt. Start with 1/2 teaspoon peppermint; you can add a little more after tasting the batter. The mint should be noticeable but not overpowering.
Add eggs: Beat in eggs one at a time on low speed, just until incorporated.
Avoid overmixing to keep air out of the batter.
Add white chocolate mixture: With the mixer on low, pour in the melted white chocolate mixture and blend until smooth. If the chocolate is too warm, it can seize or create lumps, so make sure it’s lukewarm.
Fill and smooth: Pour the batter over the crust and tap the pan on the counter a few times to release air bubbles. Run a thin knife or skewer through the batter to pop any visible bubbles.
Bake low and slow: Bake at 325°F for 50–65 minutes, until the edges are set and the center still has a slight jiggle like gelatin.
It shouldn’t ripple like liquid.
Cool gradually: Turn off the oven, crack the door, and let the cheesecake rest inside for 45 minutes. Move to a rack to cool completely, then chill uncovered for at least 6 hours (overnight is ideal). Cover once fully cold.
Make the topping: Whip the cold heavy cream with powdered sugar and vanilla to medium peaks.
Spread or pipe on top of the chilled cheesecake.
Garnish and serve: Sprinkle with crushed candy canes and add white chocolate curls if using. For clean slices, warm a sharp knife under hot water, wipe dry, and cut with firm, steady strokes.