Preheat oven to 325ºF, and lightly grease a 12 cup mini cheesecake pan with nonstick spray.
Crush the Oreos in a food processor until finely ground. Add the melted butter and mix until all the crumbs are moistened. Spoon a tablespoon of the mixture into each cavity, and use your fingers to firmly press the mixture into the bottom of each cavity. Bake crusts for 5 minutes, then remove from the oven to cool slightly.
Make the Cheesecake Batter:
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese, sugar, and cornstarch together until smooth, scraping down the sides of the bowl several times with a rubber spatula. Add the sour cream and vanilla, beating until combined. With mixer on low speed beat in eggs, one at a time, just until blended. Divide the batter evenly between two medium bowls.
Place the semi-sweet chocolate into a microwave-safe bowl and heat in the microwave until smooth and melted.*** Stir melted chocolate into one of the bowls of cheesecake batter, until combined. In a small bowl, combine the espresso powder and hot water until dissolved. Stir mixture into chocolate cheesecake batter; set aside.
Place the white chocolate into a microwave-safe bowl and heat in the microwave until smooth and melted.*** Stir melted white chocolate into the second bowl of cheesecake batter, until combined. Add the peppermint extract and a drop of red food coloring.
Spoon a tablespoon of the mocha cheesecake batter into each cavity of the pan, smoothing it into an even layer. Spoon a tablespoon of the peppermint cheesecake batter on top of the mocha batter, smoothing it out evenly. Bake in the oven for 15 minutes, or until set. Allow to cool for one hour before removing from pan. Chill in the refrigerator for at least 2 hours.
Make the Whipped Cream:
In the chilled bowl of a stand mixer fitted with a whisk attachment, beat the heavy cream until soft peaks form. Add the powdered sugar and vanilla and continue beating until stiff peaks form. Transfer to a pastry bag fitted with a star attachment (I used Wilton's 1M tip).
Pipe whipped cream onto each mini cheesecake. Top with chocolate curls and crushed peppermint candies, if desired. Serve immediately or store in the refrigerator for up to 5 days.
Notes
*If you use a muffin pan, you'll end up with about 18 cheesecakes.**Start with a 1/4 teaspoon, then add more if desired.***If you use chocolate chips, the chocolate might be a little thick and harder to melt. Just melt a teaspoon of coconut oil or vegetable oil into the chocolate to make the chocolate thinner and smoother.INSTRUCTIONS FOR CUPCAKE PAN: Line a cupcake pan with paper liners. Spoon 2 Tablespoons of the Oreo crumb mixture into each liner, using your fingers to firmly press crust into the bottom of the pan--bake for 5 minutes.Spoon enough mocha batter into the bottom of each cupcake pan until it’s halfway up the cupcake liner. Spoon peppermint batter on top of the mocha batter until it’s about a centimeter from the top of the cupcake liner. Bake in the oven for 20-23 minutes, or until set.