Preheat oven to 325°F (165°C). Grease a 9-inch springform pan.

In a medium bowl, mix together cookie crumbs, 3 tablespoons sugar, and melted butter. Press mixture into the bottom of the pan.

In a saucepan, combine raspberries, 2 tablespoons sugar, cornstarch, and water. Bring to a boil and continue boiling for 5 minutes, stirring constantly. Strain sauce through a mesh strainer to remove seeds.

In a double boiler, melt white chocolate chips with half-and-half, stirring occasionally until smooth. Remove from heat and let cool slightly.

In a large bowl, mix cream cheese and 1/2 cup sugar until smooth. Beat in eggs one at a time, then stir in vanilla and the melted white chocolate mixture.

Pour half of the batter over the crust. Spoon 3 tablespoons of raspberry sauce over the batter. Pour remaining cheesecake batter into the pan, and spoon another 3 tablespoons raspberry sauce over the top. Swirl batter with the tip of a knife to create a marbled effect.

Bake for 55 to 60 minutes, or until filling is set. Cool, cover with plastic wrap, and refrigerate for 8 hours before removing from pan. Serve with remaining raspberry sauce.