Preheat the oven to 325°F (163°C). Grease a 9-inch springform pan well on the sides and bottom. Line the base with parchment if you prefer easier release.

In a bowl, combine the Oreo crumbs and melted butter until the mixture looks like wet sand. Press evenly into the bottom of the springform pan. Bake the crust for 10 minutes. Remove and let cool while you make the filling.

Beat the cream cheese on medium speed until fully smooth and lump-free. Scrape the bowl. Add the sugar, sour cream, and vanilla. Beat again until combined.

Add eggs one at a time, mixing on low speed and scraping down the bowl between additions. Stop as soon as the eggs are incorporated — overmixing adds air and can cause cracks.

Divide the batter evenly into three bowls. Fold the melted semi-sweet chocolate into one bowl (add the cocoa powder here if using). Fold the melted milk chocolate into the second bowl. Fold the melted white chocolate into the third bowl. Use a rubber spatula and gentle motion.

Pour the batters into the crust alternately (a few spoonfuls of one, then the next) to create layered bands. Tap the pan gently on the counter to release any large air bubbles.

Bake for 60–70 minutes. The edges should be set and slightly puffed; the center should still jiggle a little when you gently shake the pan. Avoid overbaking.

Turn off the oven. Crack the oven door and leave the cheesecake inside for 1 hour to cool slowly; this reduces shrinkage and cracking.

Remove from the oven and cool to room temperature, then refrigerate for at least 4 hours or preferably overnight.

Remove the springform ring, pipe whipped cream if desired, and finish with chocolate shavings and fresh berries before serving.