Line the interior bottom and sides of a round baking pan with parchment paper (we used a 6 1/2 inch diameter and 3 inch deep round baking pan with removable bottom). You can use 2 tbsp of melted unsalted butter to stick the parchment paper onto the baking pan.
Grind enough graham crackers into fine crumbs using a food processor to get 1 cup of crumbs. In a bowl, combine the graham cracker crumbs, 4 tbsp of melted unsalted butter, and 2 tbsp of brown sugar.
Press the crumb mixture evenly onto the bottom of the baking pan until it is well-compacted and pressed evenly (you can use the back of a large spoon or the bottom of a glass to do this). Set aside in the refrigerator.
Using a mixer, beat the 2 1/4 cups of whipping cream for about 6 minutes or until stiff peaks form. Set aside in the refrigerator.
To make the matcha cheesecake layer, combine 2 1/2 tbsp of matcha powder and 4 1/2 tbsp of water in a small bowl to form a paste. Beat 8 oz of the softened cream cheese, 3/4 cup of the powdered sugar, and the matcha paste together for about 1 1/2 minute until the mixture is soft and easily easy to spread. Set aside.
To make the vanilla cheesecake layer, beat 8 oz of the softened cream cheese, 3/4 cup of the powdered sugar, and the 1 tsp of vanilla extract together for about 1 1/2 minute until the mixture is soft and easily easy to spread. Set aside.
Fold half of the whipped cream into the matcha-cream cheese mixture until well combined. Then, fold the other half of the whipped cream into the vanilla-cream cheese mixture until well-mixed.
Spread the vanilla cheesecake mixture evenly into the pan (on top of the graham cookie crust layer). Then, spread the matcha cheesecake mixture evenly on top of the vanilla cheesecake layer. Top with grated white chocolate and some more matcha powder (optional). Refrigerate for at least 3 hours before serving.