1. Preheat the oven to 325°F (160°C).
2. In a mixing bowl, combine the crushed Oreo cookies and melted butter. Press the mixture into the bottom of a 9-inch springform pan to form the crust.
3. In a separate bowl, beat the cream cheese, sugar, and vanilla extract until smooth. Add the eggs one at a time, mixing well after each addition. Stir in the sour cream.
4. Divide the cheesecake batter into three equal portions. Mix the melted semi-sweet chocolate into one portion, the melted milk chocolate into another portion, and the melted white chocolate into the last portion.
5. Pour the chocolate cheesecake batters into the prepared crust, layering them as desired. Use a knife to swirl the batters together for a marbled effect.
6. Bake the cheesecake for 70-80 minutes, or until the center is set. Let it cool completely, then refrigerate for at least 4 hours or overnight.
7. For the topping, heat the heavy cream in a saucepan until simmering. Remove from heat and add the chopped chocolates, stirring until smooth.
8. Pour the chocolate ganache over the chilled cheesecake. Sprinkle with chocolate shavings if desired.
9. Slice and serve the mouthwatering Triple Chocolate Cheesecake with Oreo Crust to impress your guests. Enjoy the rich and creamy chocolate goodness!