1. Preheat oven to 350 degrees F. Grease 9-inch springform pan; sprinkle with cookie crumbs, tapping out any excess. Refrigerate while preparing the filling.
2. Beat together cream cheese, sour cream, the 1 cup sugar, butter, cornstarch and vanilla in large bowl on low speed until mixed. Add the eggs, one at a time, beating after each addition just until combined. Do not overbeat.
3. Melt the chocolate in a small, heavy saucepan over lowest heat; stir in the remaining 2 tablespoons sugar. Remove 2 cups of batter to a clean bowl; stir in the melted chocolate and cocoa powder; the mixture will be thick.
4. Pour half of plain cheesecake batter into prepared pan. Spoon half of chocolate batter in dollops over top of plain batter. Repeat with remaining batters. Run knife through batter in figure-eight pattern to create a marble pattern.
5. Bake in 350 degrees F oven for 1 hour; center should be still soft. After first 30 minutes, cover cheesecake with aluminum foil to prevent further browning. Turn oven off. Let cheesecake stand in oven, with door closed, for 1 hour. Remove pan to wire rack, away from drafts, to cool, about 4 hours. Remove sides of pan and refrigerate overnight.