Combine the Oreo baking crumbs and melted butter until moist and crumbly.
Press the mixture into the bottom of a 9-inch springform pan and refrigerate to set.
Melt the white and semi-sweet chocolate in the microwave (break it into small pieces first) on 50% power for 30-second increments until the chocolate is just melted. Set it aside to cool slightly to just above room temperature.
Combine the room temperature cream cheese and powdered sugar in a large bowl, mixing with a hand mixer on medium speed (or in your stand mixer) until smooth.
Add the red food colouring paste and mix well, scraping down the sides of the bowl to ensure everything is incorporated and the colour is distributed evenly.
Add the melted white and semi-sweet chocolate in a steady stream while the mixer is running on low speed, until completely incorporated. Scrape down the sides of the bowl to be sure everything is incorporated. (Be sure that your cream cheese is at room temperature, otherwise the chocolate could solidify while mixing.)
Fold in the whipped cream or whipped topping by hand until the mixture is fluffy and creamy and there are no streaks of white in the batter.
Pour the cheesecake mixture into the prepared crust and smooth out the top with a rubber spatula or offset spatula.
Refrigerate to set for 6 hours or overnight, or set in the fridge for 2-3 hours and then in the freezer for 2-3 hours before serving. OR, set in the freezer only for 3-4 hours.