Heat a medium sauté pan over medium heat, add half of the butter (8 tablespoons) and allow to melt.
Continue to cook, stirring constantly, until the butter turns deep golden brown and small brown bits form at the bottom, about 10 minutes. Immediately pour the butter into a small bowl to stop the cooking process. Let cool to room temperature, about 20 minutes.
In a medium mixing bowl whisk together the flour, salt and baking soda and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the remaining butter and brown sugar together. Beat in the vanilla extract and the miso.
Add the cooled brown butter and granulated sugar and continue to beat until smooth. Add the eggs, one at a time, beating well after each addition. Gradually add the dry ingredients until it has all been incorporated.
Fold in the white chocolate chips using a spatula. Cover and refrigerate the dough, for at least 1 hour before baking.
When ready to bake, preheat the oven to 350ºF (180ºC). Line two baking sheets with parchment paper. Scoop the dough in two-tablespoon size balls, placed 2-inches apart.
Bake for 10 to 12, minutes until cookies are golden brown. Remove and let cool on wire racks.