Preheat your oven to 325°F (163°C). Lightly grease a 9×9-inch baking pan and set it aside. For easier removal, you can also line the pan with parchment paper.
In a double boiler over medium-low heat, melt the chopped white chocolate and butter together. Stir continuously to ensure the white chocolate melts evenly without burning. Once melted and smooth, remove the mixture from the heat.
In a large mixing bowl, whisk together the eggs, egg yolks, granulated sugar, and vanilla extract until the mixture is pale and smooth. For an easier and faster process, you can use an electric hand mixer on high speed.
Slowly pour the melted white chocolate and butter mixture into the egg mixture, whisking until fully combined and smooth.
Using a rubber spatula, gently fold the all-purpose flour and salt into the wet ingredients just until combined. Be careful not to overmix.
Pour the white chocolate brownie batter into the prepared pan. Use a mini offset spatula or the back of a spoon to smooth the batter evenly in the pan.
Bake the brownies in the preheated oven for 29-33 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out clean.
Once baked, allow the brownies to cool completely in the pan on a wire rack.
Once cool, use a butter knife to loosen the edges of the brownies from the pan. Turn the pan over to gently release the brownies. Cut into 16 squares and enjoy!