Mix the chocolate cookie crumbs with melted butter until the mixture resembles wet sand. Press evenly into the bottom of a 9-inch springform pan. Refrigerate to chill while preparing the filling.
In a large bowl, beat the softened cream cheese and sugar until smooth and creamy. Add vanilla extract. Beat in eggs one at a time, mixing well after each. Stir in sour cream until incorporated. Fold in melted semi-sweet chocolate chips until uniform.
Pour the cheesecake batter over the chilled crust. Smooth the top with a spatula. Bake at 325°F (163°C) for 50-60 minutes until edges are set but center jiggles slightly. Turn off oven, crack door open, and cool cheesecake inside for 1 hour.
Melt white chocolate chips with heavy cream in a microwave-safe bowl or double boiler. Optionally add black food coloring for contrast. Transfer mixture to a piping bag or plastic bag with a small corner cut off.
Once cheesecake is completely cooled, pipe concentric circles of white chocolate on the surface. Drag lines from center outwards with a toothpick or skewer to create a spiderweb effect, alternating directions for authenticity.
Drizzle chocolate syrup over the top decoratively. Chill cheesecake at least 4 hours or overnight to set spiderweb and flavors.
