Heat the butter in a small pot or saucepan, and let it cook for 2-3 minutes over medium heat, letting it brown and turn nutty, and making sure it doesn’t burn at the bottom. Pour the brown butter through a sieve into a heatproof bowl, and add the white chocolate, sugar, and salt to it. Whisk everything together, melting the chocolate and dissolving the sugar. Then, add in the eggs and vanilla extract, and mix to incorporate. Sift the flour and matcha powder into the wet ingredients, and whisk for 1 minute until a thick, smooth batter forms, and no streaks of flour remain. (Make sure not to overmix the batter at this point.)
Chocolate batter
Similar to the matcha batter, first start off by melting the butter and chocolate in a bowl (you can do this in a pot, or in a microwave too). Then, whisk in the sugar and salt, then the eggs and vanilla extract. Finally, add in the flour, cocoa powder, and espresso powder, and fold until just mixed and no streaks of flour remain.
Prepping
Heat your oven to 180°C. Meanwhile, brush (or spray) a 9’’ x 9’’ baking tin (or one of a similar size) with oil, then line it with baking paper.
Marbling
Reserve roughly 1/4 of the chocolate batter in a bowl. Pour the rest of the chocolate batter into the lined baking tin, spreading it out to all sides, and smoothing the top with a spatula. Then, pour all of the matcha batter on top of the chocolate batter, and spread it out evenly again. Now, dollop on the chocolate batter you saved onto the matcha batter (I find a 3x3 grid of dots works well). Using a toothpick or a chopstick, gently swirl and circle your way through the batter to form a marbled effect.
Baking
When brownie base is marbled to your desire, pop the brownie into the oven and bake for 25-30 minutes, or until a cake tester poked through it comes out clean. When done, let the brownie cool in the tin for 10 minutes, before removing it from the tin and setting it on a wire rack to continue cooling to room temperature. Slice it up into pieces, and serve with ice cream, whipped cream, or just devour it on its own!