Preheat the oven to 350°F (175°C).

Make the crust: Place the 28 Oreo cookies in a food processor and pulse until they are fine crumbs. Add the 4 tablespoons melted unsalted butter and 1 pinch salt; pulse or mix until the crumbs are evenly moistened.

Press the crumb mixture into the bottom and up the sides of a 9-inch springform pan (or similar), using the bottom of a flat glass or measuring cup to make an even, compact crust. Bake the crust on the middle rack for 10 minutes. Remove from the oven and let the crust cool completely on a wire rack.

Prepare the filling: Put the 2 pounds softened cream cheese in the bowl of a stand mixer fitted with the paddle attachment. Beat at medium-high speed for about 1 minute, then scrape down the sides and bottom of the bowl.

Add the 1 1/2 cups granulated sugar and the 8 ounces sour cream. Mix at medium-low speed just until combined. Scrape the bowl again.

Add the 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 until the batter is smooth and fairly runny. Scrape the bowl once more to ensure even mixing.

Fold in the 3/4 cup crushed peppermint candies and the 3/4 cup chopped white chocolate with a rubber spatula until evenly distributed in the batter.

Wrap the outside of the prepared springform pan with four sheets of 18-inch heavy-duty aluminum foil so the bottom and sides are completely covered and water cannot seep in. Set the wrapped pan in a deep roasting pan or a baking sheet with sides about 2 inches deep.

Pour the cheesecake batter into the cooled crust and smooth the top. Place the roasting pan with the wrapped springform pan on the lower third oven rack.

Carefully pour very hot water into the roasting pan until it reaches about 1 1/2 inches up the sides of the springform pan (be careful to avoid splashing water into the cheesecake).

Bake at 350°F for 1 to 1 1/2 hours. After about 60 minutes, check the center: the cheesecake should be set at the edges and slightly jiggly in the center but not liquid. If the center is still very liquid, continue baking and check again in 10–15 minutes.

When the cheesecake is set but still slightly jiggly in the center, turn the oven off and leave the cheesecake inside with the oven door closed for 1 hour to cool gradually.

After the hour, remove the roasting pan from the oven, carefully lift the wrapped springform pan out of the water, and remove the foil. Let the cheesecake cool to room temperature, then refrigerate for at least 6 hours (preferably overnight) to fully set.

Before serving, run a knife around the edge of the pan to release the cheesecake, remove the springform ring, slice, and serve.