Heat the oven to 175 C / 350 F with a rack in the center. Line a 20 cm / 8-inch square metal baking pan with parchment, leaving an overhang on two sides so the bars lift out. Melt the butter and let it cool for 5 minutes.

In a 2.8 L / 3-quart bowl, whisk the melted butter with both sugars for 1 minute until glossy with no dry lumps. Add the egg, yolk, and vanilla, and whisk for another minute until the mixture is smooth and slightly thickened.

Sift the flour, matcha, baking powder, and salt over the bowl. Fold with a silicone spatula until only a few dry streaks remain, then fold in 130 g of the chopped white chocolate. Stop mixing as soon as the streaks disappear.

Scrape the thick batter into the pan and press it level into the corners with a damp spatula. Scatter the remaining 40 g of white chocolate over the top.

Bake for 25 to 28 minutes, until the edges are set, the center barely jiggles, and a toothpick comes out with a few moist crumbs. Don't wait for a clean toothpick, or the bars will dry out and the green will turn olive.

Cool in the pan on a wire rack for 60 minutes. Lift out by the parchment, then cut into 16 squares, wiping the knife clean between cuts.