Mix together the cookie crumbs, 3 tablespoons of sugar, and melted butter in a medium bowl. Press this into the bottom of a 9-inch springform pan.
Combine raspberries, 2 tablespoons sugar, cornstarch, and water in a medium pot. Bring to a boil and boil for 5 minutes while the sauce thickens up. Strain the sauce through a mesh strainer to remove any seeds.
Preheat oven to 325°F. Melt white chocolate chips and half and half in a medium pot on low heat, stirring constantly until smooth.
Mix together cream cheese and 1/2 cup sugar in a large bowl until smooth. Add eggs one at a time and beat. Add vanilla and melted white chocolate and mix well.
Pour half the batter over the crust, then 3 tablespoons of the raspberry mixture over the batter. Pour the remaining batter into the pan and spoon 3 tablespoons of the raspberry sauce on top. Create a marbled effect by swirling the batter with the tip of a knife.
Bake the cheesecake for 55 to 60 minutes or until the filling is set.
Cover with plastic wrap and refrigerate for 8 hours before removing from the pan. Serve the cheesecake with the leftover raspberry sauce.