In a heat-proof bowl over barely simmering water, melt the white chocolate and butter. Stir occasionally. Let it cool for a couple of minutes afterward.
In a mixer fitted with a paddle attachment, mix the softened cream cheeses until smooth and fluffy, scraping down the sides to eliminate lumps. Add the sugar and mix until smooth. With the mixer running, add the eggs one at a time, mixing well each time to ensure eggs are well-incorporated. Pour in the heavy cream and melted chocolate and add the green tea powder, mixing them all until smooth and green tea is well-blended, scraping down the sides a few times, if needed. There may be a spot of green tea here and there but that’s fine.
Transfer the mixture to the prepared pan. Increase the oven temperature to 325F.
Wrap the springform pan in heavy foil going up at least an inch above the edge of the pan. Ensure there's no tear anywhere so water doesn't seep through. Place the springform pan in a bigger pan and fill the latter with hot water up to the middle of the springform pan. Bake for 1 hour and 10 minutes.
Remove to a rack and let cool in the pan completely. Refrigerate overnight. I suggest making this 2 days ahead to develop more flavor. After 2 days the green tea taste would have mellowed down and provides a nice contrast to the white chocolate. It would just be the perfect balance of flavor by then. A subtle hint of green tea and then the sweetness of the chocolate plus the creaminess of the cheese all harmoniously work together to form such a wonderfully luscious and extraordinary cheesecake!
Serve this with some fresh berries as they complement the cheesecake very well.