Preheat your oven to 325°F. Lightly grease a 9×9-inch pan or line it with parchment paper for easy removal.
Melt the butter and white chocolate together in a double boiler over medium-low heat, stirring constantly until smooth. Remove from heat.
In a large bowl, whisk together the eggs, egg yolks, sugar, and vanilla until pale and smooth. Using an electric hand mixer on high speed can make this easier.
Pour in the melted white chocolate mixture and whisk until well combined.
Gently fold in the flour and salt using a rubber spatula until just combined.
Pour the batter into the prepared pan and smooth the top with a spatula.
Bake for 29-33 minutes. Let the brownies cool completely in the pan on a wire rack.
Once cool, use a butter knife to loosen the edges, then gently turn the brownies out of the pan. Cut into 16 squares and enjoy!