Pre-heat the oven to 350f degrees & line an 8x8 inch square baking pan with parchment paper
In the bowl of your stand mixer fitted with the paddle attachment, beat cream cheese & sugar on medium speed until smooth, stopping to scrape the bowl with a spatula the bowl as needed
Stop the mixer & sift the matcha into the cream cheese & beat until fluffy, a few minutes
Add in the melted white chocolate & egg, beat until mixture is well combined
In a medium saucepan, melt butter over medium heat. Turn heat to low, add chocolate & stir until just melted. Remove from heat & whisk in the sugar. Whisk in eggs, vanilla, sweet rice flour, tapioca starch, cocoa powder & salt, 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 & matcha cheesecake into a marbled pattern.
Bake the brownies on the center 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.
Brownies will last 2 days at cool room temperature, 5 days in the refrigerator, or 1 month double wrapped in the freezer.