Preheat the oven to 350 degrees F (180 degrees C) and line an 8 by 8-inch square baking pan with parchment paper.
In the bowl of your stand mixer fitted with the paddle attachment, beat Cream Cheese (8 ounce) and Granulated Sugar (1/4 cup) on medium speed until smooth, stopping to scrape the bowl with a spatula the bowl as needed.
Stop the mixer and sift the Matcha Powder (1 tablespoon) into the cream cheese and beat until fluffy, a few minutes. Add in the White Chocolate (4 ounce) and Egg (1) beat until mixture is well combined.
In a medium saucepan, melt Unsalted Butter (6 tablespoon) over medium heat. Turn heat to low, add Semi-Sweet Baking Chocolate (5.5 ounce) and stir until just melted. Remove from heat and whisk in the Granulated Sugar (1/2 cup).
Whisk in Egg (2), Vanilla Extract (1 teaspoon), Sweet Glutinous Rice Flour (1/2 cup), Tapioca Flour (1 tablespoon), Unsweetened Cocoa Powder (1 tablespoon), and Salt (1/4 teaspoon), mix until well combined.
Portion about 3/4 of brownie batter into the prepared pan. Add the matcha cheesecake to the top of the brownie batter in an even layer.
Add the remaining 1/4 of the brownie batter to the top of the matcha cheesecake layer in tablespoon dollops. Use the tip of a paring knife to swirl the brownie batter and matcha cheesecake into a marbled pattern.
Bake the brownies on the centre rack for 30 minutes. Let the brownies cool completely in the pan. Lift the brownies out of the pan by the parchment paper. Slice into 9 or 16 squares, depending on how large you want your slices.