Preheat oven to 325°F. Spray a 9-inch square baking pan with nonstick spray and set aside.
In a small saucepan over low heat, melt the butter and the chopped white baking chocolate, stirring frequently until smooth. Remove from heat and let cool 2–3 minutes, until warm but not hot.
In a medium bowl, whisk the eggs, granulated sugar, and vanilla extract until combined and slightly smooth.
Slowly add the warm chocolate-butter mixture to the egg mixture, stirring constantly until fully combined.
Add the all-purpose flour and 1/4 teaspoon salt to the mixture and stir until just combined and no dry flour remains.
Fold in the chopped macadamia nuts and the milk chocolate chips until evenly distributed.
Pour the batter into the prepared pan and spread it into an even layer.
Bake for 30 to 35 minutes, or until the top is lightly browned and a toothpick inserted near the center comes out with a few moist crumbs (not wet batter).
Remove from the oven and cool the pan on a wire rack. Once completely cooled, cut into bars.