Beat together the cream cheese and sugar in a very large bowl. Beat until the mixture is very smooth and no lumps remain.
Whisk together the eggs in a small bowl. With the mixer on low speed, mix the eggs into the cream cheese mixture about 1/2 at a time. Turn off the mixer and scrape down the sides of the bowl.
Divide the batter evenly into 2 bowls and set aside.
Finely chop the dark chocolate until its in very small pieces and place in a heatproof bowl. Do the same with the white chocolate, and place in a second heatproof bowl.
Heat the cream until almost boiling (either in the microwave or a double boiler).
Pour half the cream over the dark chocolate and half the cream over the white chocolate. Let each bowl sit for 3-5 minutes, then whisk each until smooth. If the chocolate in either bowl isn't quite melted, microwave the bowl on medium power for 45 seconds and whisk until smooth.
Place the springform pan with the baked crust (still wrapped in aluminum foil) in the middle of a large roasting pan.
Stir the melted dark chocolate mixture into one bowl of the cream cheese batter until the mixture is smooth. Pour over the crust.
Stir the white chocolate mixture into the other bowl of the batter. Very carefully spoon the white chocolate cheesecake batter over top of the chocolate cheesecake layer. Do not pour or dump the white chocolate batter over the dark chocolate layer, otherwise, you'll disturb the dark chocolate layer.