Preheat the oven to 350 degrees and line a small square baking pan with parchment paper.
Melt the butter and dark chocolate together in a heatproof bowl over simmering water or in short microwave bursts until smooth.
Stir the granulated sugar into the chocolate mixture until combined, then add the eggs one at a time followed by the vanilla extract.
Mix in the flour and salt until just combined, then pour the batter into the prepared pan and smooth the top.
In a separate bowl, beat the cream cheese with the powdered sugar and matcha powder until uniform in color.
Drop spoonfuls of the matcha mixture over the brownie batter and use a knife to swirl it through gently.
Bake for 25 to 30 minutes until the edges are set and a toothpick comes out with a few moist crumbs.
Cool completely in the pan before cutting into squares.