Heat oven to 325 degrees Fahrenheit and grease a 9-inch springform pan with parchment bottom.
Press crushed Oreos and melted butter firmly into pan bottom, baking for 8 minutes, then cool.
Beat cream cheese and sugar until smooth, then beat in eggs and sour cream on low speed.
Divide batter in half, stirring melted dark chocolate into half and melted white chocolate into remaining half.
Pour dark chocolate batter into crust, gently smoothing white chocolate batter over top.
Bake for 60 minutes until edges are set, then turn off oven and let rest inside for 1 hour.
Chill in refrigerator for 6 hours before slicing neatly.