In a small bowl, combine the graham cracker crumbs and the melted butter until the crumbs are completely moistened.
Press the crumb mixture into the bottom of a 9-inch springform pan and up the sides just slightly, to form a crust. Chill to set.
Beat the cream cheese on medium speed until very smooth. The cream cheese MUST be at room temperature.
Add the powdered sugar and Matcha powder, and beat well until everything is well combined and no streaks of Matcha powder remain.
Melt the white chocolate in the microwave (break it into small pieces first) on 50% power for 30-second increments until the chocolate is just melted.
Let the chocolate cool slightly to just above room temperature before pouring it into the cream cheese mixture. The cream cheese mixture MUST be at room temperature or it will cause the chocolate to solidify during the mixing process, creating chunks chocolate in the cheesecake batter (the cheesecake will lose its silky smooth texture).
Beat on medium speed until the chocolate is fully incorporated (scrape down the sides of the bowl well here).
Fold in the whipped cream or whipped topping gently until fully incorporated.
Pour the batter into the prepared crust and smooth out the top with a spatula.
Chill the cheesecake in the fridge overnight, (OR for at least 6 hours plus 1 hour in the freezer) before slicing and serving.
Serve with a dollop of whipped cream, white chocolate shavings, and a dusting of Matcha powder (if desired).