For the crust: In a medium-sized bowl, combine the chocolate cookie crumbs, melted butter, and sugar. Stir until the mixture is evenly blended, then press it firmly into the bottom of a 9-inch springform pan to form the crust base.

For the raspberry sauce: In a saucepan, mix together the frozen raspberries, water, sugar, and cornstarch. Bring the mixture to a boil and continue boiling for about 5 minutes, or until the sauce thickens. Strain the sauce through a fine mesh sieve to remove the seeds. Set aside. Preheat your oven to 325°F (165°C).

For the cheesecake filling: Place the white chocolate chips and half-and-half cream in a metal bowl set over a pot of simmering water (double boiler method). Stir occasionally until the chocolate is melted and the mixture is smooth.

In a large mixing bowl, beat the softened cream cheese and sugar together until creamy and smooth. Add in the eggs one at a time, beating well after each addition. Mix in the vanilla extract, then gently blend in the melted white chocolate mixture. Pour half of the batter over the prepared crust.

Drizzle 3 tablespoons of the raspberry sauce over the cheesecake layer. Pour the remaining batter on top, followed by another 3 tablespoons of raspberry sauce. Use the tip of a knife to swirl the sauce into the batter, creating a marbled pattern.

Place the cheesecake in the preheated oven and bake for 55 to 60 minutes, or until the filling is set. Allow the cheesecake to cool at room temperature. Once cooled, cover it with plastic wrap and refrigerate for at least 8 hours or overnight to fully chill and set.

When ready to serve, remove the cheesecake from the springform pan and garnish each slice with the remaining raspberry sauce.