In a medium bowl, mix together cookie crumbs, 3 tablespoons sugar, and melted butter. Press mixture into the bottom of a 9 inch springform pan.
In a saucepan, combine raspberries, 2 tablespoons sugar, cornstarch, and water. Bring to boil, and continue boiling 5 minutes, or until sauce is thick. Strain sauce through a mesh strainer to remove seeds.
Preheat oven to 325 degrees F (165 degrees C). In a metal bowl over a pan of simmering water, melt white chocolate chips with half-and-half, stirring occasionally until smooth.
In a large bowl, mix together cream cheese and 1/2 cup sugar until smooth. Beat in eggs one at a time. Blend in vanilla and melted white chocolate. Pour half of batter over crust. Spoon 3 tablespoons raspberry sauce over batter. Pour remaining cheesecake batter into pan, and again spoon 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.
