Cook butter in a medium saucepan over medium heat, stirring often, until it foams, then browns for about 5–8 minutes. After it has browned, turn off the heat and remove the butter into separate bowl. Let it cool completely before using.
Preheat oven to 350F/180°C. Grease an 8x8-inch/20x20cm square pan and line the bottom with parchment paper. Set aside.
In a large bowl, combine together all purpose flour, matcha powder, baking powder, and salt. Set aside.
In a large bowl, whisk together cooled brown butter, brown sugar, and granulated sugar until well combine. Whisk in eggs and vanilla extract until well combined.
Add dry ingredients to wet ingredients and mix until well incorporated with a spatula.
Pour and spread the batter evenly into the prepared pan. Top the brownies with strawberry slices and white chocolate chunks.
Bake for 25 minutes or until a toothpick inserted in the center comes out with a couple of moist crumbs. Cool completely in the pan before slicing.