Step 1: Prepare the Oreo Crust

1. Preheat your oven to 325°F (160°C).
2. Crush Oreo cookies into fine crumbs using a food processor or by placing them in a zip-top bag and using a rolling pin.
3. Combine Oreo crumbs with melted butter in a mixing bowl. Stir until the mixture resembles wet sand.
4. Press the mixture firmly into the bottom of a greased 9-inch springform pan to form an even crust.
5. Bake the crust for 8 minutes. Remove from the oven and let cool.

Step 2: Make the Peppermint Cheesecake Filling

1. In a large bowl, beat the softened cream cheese and sugar together until smooth and creamy.
2. Add eggs, one at a time, mixing well after each addition.
3. Mix in sour cream, vanilla extract, and peppermint extract until fully combined.
4. If desired, add red food coloring and gently swirl it into the batter for a festive touch.

Step 3: Assemble and Bake

1. Pour the cheesecake filling over the cooled Oreo crust, smoothing the top with a spatula.
2. Place the springform pan on a baking sheet. Bake in the preheated oven for 55-60 minutes, or until the center is slightly jiggly but set.
3. Turn off the oven and let the cheesecake cool inside with the door slightly open for 1 hour. This helps prevent cracking.

Step 4: Chill and Decorate

1. Once cooled to room temperature, refrigerate the cheesecake for at least 4 hours, or preferably overnight.
2. Before serving, spread whipped cream over the top and sprinkle with crushed candy canes, chocolate chips, or shavings for garnish.