01 - Preheat oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper, allowing an overhang for easy removal.
02 - Combine unsalted butter and semisweet chocolate chips in a heatproof bowl. Melt together using a microwave in 30-second intervals or over a bain-marie, stirring until smooth. Allow mixture to cool slightly.
03 - Whisk granulated sugar, eggs, and vanilla extract into the cooled chocolate mixture until combined. Fold in all-purpose flour and salt until just incorporated. Set aside.
04 - In a separate bowl, beat cream cheese and granulated sugar until smooth and creamy. Add egg, all-purpose flour, matcha powder, and vanilla extract; beat until fully combined and smooth.
05 - Spread two-thirds of the brownie batter evenly in the prepared pan. Spoon the matcha cheesecake mixture in several dollops over the brownie layer. Add remaining brownie batter in between.
06 - Gently swirl the brownie and matcha cheesecake mixtures together with a skewer or knife to create a marbled effect.
07 - Bake for 35 minutes, or until the edges are set and the center is just slightly jiggly. Cool completely in the pan, then lift out using the parchment overhang and slice into squares.