Preheat your oven to 325°F (165°C). Line your 9x9 baking pan with parchment paper, leaving some overhang on two sides so you can easily lift the finished brownies out.
Melt the Base: Combine the butter pieces and chopped white chocolate bar in a microwave safe bowl. Heat in 20-second increments, stirring well after each. It's ready when it's completely smooth and glossy. It's easy to burn white chocolate, so don't rush this step.
Whisk Sugar and Eggs: In a separate large bowl, vigorously whisk the sugar, eggs, and egg yolk together until the mixture turns a pale yellow color. This takes about 30 seconds by hand or 15 seconds with an electric mixer on high. You're looking for a light, frothy texture.
Combine the Mixtures: Stir the vanilla extract into the egg mixture, then pour in the melted butter and white chocolate. Stir slowly but thoroughly until the batter is completely homogeneous.
Add the Dry Ingredients: In a small bowl, whisk the flour, salt, and baking powder together. Dump this into the wet mixture and fold it in with your spatula until just combined. Don't overmix here—a few small streaks of flour are okay. Overmixing develops gluten and can make the brownies tough.
Fold in the Chips: Gently fold in the white chocolate chips until they're evenly distributed. Spread the thick batter evenly into your prepared 9x9 pan. It will be very thick—use the spatula to coax it into the corners.
Bake: Place the pan on the center rack of your preheated oven. Bake for exactly 42 minutes. The top should be a beautiful golden brown. A toothpick inserted into the center should come out clean or with a few moist, fudgy crumbs. If it comes out wet with raw batter, give it 2-3 more minutes.
Cool (This is the Hard Part): Allow the brownies to cool completely in the pan on a wire rack. I know it's tempting, but slicing them warm will result in a gooey, messy center. If you don't mind that, then dive right in! Otherwise, patience gives you perfect, clean slices.