PREPARE THE SAUCE: Press the raspberries and their syrup through a sieve into a saucepan. Add the corn syrup, lemon juice and cornstarch mixture. Bring to a boil, stirring often, then simmer for 1 to 2 minutes. Pour into a bowl and cool, then chill.
In a large saucepan, combine the milk and 1 cup of the cream and bring to a boil. In a bowl, beat the egg yolks and sugar with a hand-held mixer for 2 to 3 minutes until thick and creamy. Gradually pour the hot milk mixture over the yolks, then return to the pan. Cook over medium heat until the custard coats the back of a wooden spoon, stirring constantly.
Remove the pan from the heat and stir in the white chocolate until melted and smooth. Pour the remaining cream into a large bowl. Strain in the hot custard, mix well, then stir in the vanilla extract. Cool, then transfer the custard to an ice cream maker and freeze according to the manufacturer's instructions.
When the mixture is frozen, but still soft, transfer 1/3 of the ice cream to a freezerproof bowl. Set 1/2 the raspberry sauce aside. Spoon a third of the remainder over the ice cream. Cover with another third of the ice cream and more sauce. Repeat. With a knife or spoon, lightly marble the mixture. Cover and freeze. Allow the ice cream to soften for 15 minutes before serving with the remaining raspberry sauce.
* If you like, you can substitute a 10 oz jar of reduced-sugar raspberry preserves or jam for the frozen raspberries.
If using the preserves, omit the 1 T. cornstarch, but still add the 1 T. water when making the sauce.