Weigh your ingredients with a kitchen scale.
Gather all the ingredients. Make sure the eggs are at room temperature.
Preheat the oven to 325°F (160ºC). Line an 8-inch (20-cm) square cake pan with parchment paper.
Add 8 oz white chocolate to a large, heatproof mixing bowl. Break it into smaller pieces.
Sift 1⅔ cups confectioners’ sugar into a separate bowl. Sift in ½ cup light brown sugar and mix the two sugars with a whisk.
Slice 1 cup unsalted butter into thick pats and place in a light-colored skillet. Cook on medium heat, stirring occasionally, until the butter bubbles and foams, about 3 minutes.
Continue cooking, stirring occasionally, until the milk solids start to form on the bottom of the pan. Cook until the butter turns a warm amber color and milk solids are dark golden brown, about 2 minutes. Remove from the heat and stir as it cools in the pan for 3 minutes.
Pour the warm brown butter over the white chocolate. Mix gently with a spatula until melted and smooth.
Sift 6 Tbsp matcha into the chocolate mixture using a fine-mesh strainer. Whisk until evenly blended and smooth.
Add the sugars and stir thoroughly until they are fully dissolved and the mixture looks glossy and smooth.
Crack 4 large eggs into a small bowl, then add them to the batter. Whisk gently until fully incorporated.
Add 1 tsp salt and mix gently until smooth.
Sift 1 cup all-purpose flour into the batter. Gently fold with a spatula until just combined.
Pour batter into the lined baking pan and smooth the top. Bake on the middle rack for 45–50 minutes or until a toothpick inserted in the center comes out with moist crumbs.
Cool in the pan for at least 1 hour at room temperature. Cut into squares and serve.
