In a double boiler, melt together the ⅓ cup whipping cream and 1 cup of white chocolate chips.
You want this just at the melting point, so be careful not to overheat.
Let it cool to lukewarm, if necessary, after melting; set aside to cool while you prepare the rest of the cheesecake batter.
In a medium bowl, cream together the cream cheese and ½ cup sugar for a few minutes, scraping the bowl often.
Add the eggs, one at a time, beating well after each addition.
Stir in the vanilla extract and melted white chocolate.
Finally blend in the 1 cup of whipping cream until smooth.
Pour over the prepared base, place in pre-heated oven and bake in a bain marie (see note below) at 325°F for 60 to 70 minutes.
The cheesecake may be beginning to lightly brown at the edges but a cheesecake does not need to brown at all to be fully baked.
The surface of the cheesecake should lose any shine when the cake is properly baked; it can still be slightly wobbly just at the center at this point.
Remove the cake from the oven and run a sharp knife completely around the edge of the pan; this will allow for the cheesecake to shrink as it cools and hopefully not crack.
Allow the cheesecake to cool thoroughly, on a wire rack, at room temperature.
Be mindful to never put a hot cheesecake into the fridge to cool quickly; this may result in an under baked cheesecake because the residual heat actually continues to set the cheesecake after it comes out of the oven.