Preheat the oven to 325°F (165°C) and line a 9×9” baking pan with parchment paper, then set it aside. In a microwave-safe bowl, combine the butter and chopped white chocolate pieces. Heat in 20-second increments, stirring in between, until the mixture is fully melted and smooth.
In a separate bowl, whisk together the sugar, eggs, and egg yolk until pale yellow (about 30 seconds; alternatively, you can use an electric mixer on high speed for about 15 seconds). Stir in the vanilla extract, then add the melted chocolate mixture and mix until fully combined.
In another bowl, whisk together the flour, salt, and baking powder. Add this dry mixture to the white chocolate mixture and stir until thoroughly incorporated.
Use a spatula to fold in the white chocolate chips, then spread the batter evenly into the prepared baking pan. Transfer the pan to the center rack of the preheated oven and bake for 42 minutes, or until a toothpick inserted into the center comes out clean or with moist crumbs.
Allow the brownies to cool before slicing and serving (they may appear underbaked or gooey in the center if sliced too soon, but if you don’t mind this, feel free to enjoy them right away!).