Preheat your oven to 325°F (163°C). In a medium bowl, combine 1 1/2 cups of chocolate cookie crumbs with 1/2 cup melted unsalted butter. Stir until the crumbs are evenly coated and resemble wet sand. Press this mixture firmly into the bottom of a 9-inch springform pan, creating an even layer. Bake the crust for 10 minutes, then remove and let it cool while you prepare the filling.
In a large mixing bowl, beat 2 cups of softened cream cheese until smooth and creamy. Gradually add 1 cup granulated sugar and 1 teaspoon vanilla extract, mixing well after each addition. Add the 3 large eggs one at a time, beating gently after each to avoid incorporating too much air. Then, blend in 1 cup sour cream and 1/2 cup unsweetened cocoa powder until the mixture is smooth and uniformly chocolatey.
Using a spatula, gently fold in 1 cup each of semi-sweet, white, and milk chocolate chips. This triple chocolate combination creates delightful pockets of melting sweetness throughout the cheesecake.
Pour the cheesecake batter over the cooled crust, spreading it evenly. Prepare a water bath by placing the springform pan inside a larger roasting pan. Pour hot water into the roasting pan until it reaches halfway up the side of the springform pan. Wrap the bottom of the springform pan with aluminum foil to prevent leaks. Bake at 325°F (163°C) for 60-70 minutes, or until the edges are set but the center still jiggles slightly.
Remove the cheesecake from the water bath and let it cool to room temperature on a wire rack. Once cooled, refrigerate for at least 4 hours—or overnight—to allow the flavors to meld and the texture to firm up perfectly.