In a medium bowl, mix together the cookie crumbs, 3 tablespoons sugar, and melted butter. Press mixture into the bottom of a 9 inch springform or other circular pan.
In a saucepan, combine the raspberries, 2 tablespoons sugar, cornstarch, and water. Bring to a boil and keep it boiling for 5 minutes, or until the sauce is thick. Strain sauce through a mesh strainer or cheesecloth to remove seeds.
Preheat oven to 325F. 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, then 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. To create a marbled effect you can gently trace a hash sign over the top with the point of a knife. First make all lines in one direction, then cross the lines perpendicularly.
Wrap foil around the bottom of your pan and place the pan on a cookie sheet. Then fill the cookie sheet with water and bake the cheesecake for an hour. Then turn the oven off and let the cheesecake sit in the oven for another hour. This prevents the cake from sinking in the middle.
