Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners and set aside.
Make the Oreo crust
Place 16 Oreo cookies in a food processor and pulse until finely crushed. Transfer the crumbs to a bowl and stir in ¼ cup melted butter until evenly combined. Spoon about 1½ tablespoons of the mixture into each muffin cup and press firmly into the bottom to form the crust.
Prepare the cheesecake filling
In a large mixing bowl, combine 1 cup cream cheese, ½ cup heavy cream, ¾ cup powdered sugar, 3 eggs, 1 teaspoon vanilla extract, and ½ teaspoon peppermint extract. Mix until smooth and fully blended, scraping down the sides of the bowl as needed. Gently fold in ¼ cup crushed peppermint candies.
Fill and bake
Divide the cheesecake filling evenly over the prepared crusts, filling each liner nearly full. Bake for 25 minutes, or until the centers are set and no longer jiggly.
Cool and chill
Remove the pan from the oven and let the mini cheesecakes cool in the pan for about 30 minutes. Transfer to the refrigerator and chill for at least 3 hours, or until completely set.
Melt the white chocolate
Place ½ cup white chocolate chips in a microwave-safe bowl. Microwave in 20-second intervals, stirring well after each interval, until smooth and fully melted. Take care not to overheat, as white chocolate can scorch easily.
Decorate and serve
Just before serving, top each mini cheesecake with whipped cream, drizzle with the melted white chocolate, and finish with a sprinkle of crushed peppermint candies.