Preheat the oven to 350°F.
Place 28 regular Oreo cookies in a food processor and pulse until they become a fine crumb.
Add 4 tablespoons melted unsalted butter and 1 pinch salt to the crumbs and pulse or mix until evenly combined.
Press the crumb mixture firmly and evenly into the bottom and up the sides of a springform pan (use the bottom of a flat glass or measuring cup to get an even crust).
Bake the crust at 350°F for 10 minutes. Remove from the oven and allow the crust to cool completely. While the crust cools, clean and dry the springform pan exterior if needed.
When the crust is cool, preheat the oven to 350°F again.
In the bowl of a stand mixer fitted with the paddle attachment, add 2 pounds softened cream cheese. Beat on medium-high speed for about 1 minute, then scrape down the sides and bottom of the bowl and beat briefly again until very smooth and lump-free.
Add 1 1/2 cups granulated sugar and 8 ounces sour cream. Mix on medium-low speed until just combined. Scrape the bowl and mix 10 more seconds.
Add 5 large eggs and beat on low speed until just combined, about 30 seconds to 1 minute. Scrape the bowl.
Add 1 teaspoon vanilla extract and 1 teaspoon peppermint extract. Beat on low speed only until the mixture is smooth and incorporated.
Fold in 3/4 cup crushed peppermint candies and 3/4 cup chopped white chocolate by hand (do this right before pouring the batter into the crust).
Wrap the outside of the springform pan with four sheets of 18-inch heavy-duty aluminum foil, covering the base and sides to create a waterproof barrier.
Place the wrapped springform pan into a deep roasting pan or a baking sheet with sides at least 2 inches high. Pour the cheesecake batter into the prepared crust.
Carefully pour very hot (not boiling) water into the roasting pan until the water reaches about 1 1/2 inches up the outside of the springform pan to create a water bath.
Bake on the lower third rack at 350°F for 1 to 1 1/2 hours. After about 1 hour, check doneness: the edges should be set and the center should still have a slight jiggle (not liquid). If very liquid, continue baking and check again in 10–15 minute increments.
When the cheesecake is firm at the edges but still slightly jiggly in the center, turn the oven off and leave the cheesecake inside with the oven door closed for about 1 hour to cool slowly.
Remove the springform pan from the water bath, unwrap and discard the foil, and transfer the cheesecake to the refrigerator. Chill until fully set, at least 6 hours (or overnight).
Before serving, run a knife around the inside edge of the springform to loosen the cheesecake, release the side of the pan, and remove it. Garnish as desired and slice to serve.