Preheat oven to 350 degrees. In a medium saucepan melt the butter, swirling and stirring the butter until nicely browned bits appear in the bottom of the pan. This may take about 5-7 minutes. Once the butter is browned, remove pan from heat and set aside to cool a bit while you measure out the dry ingredients and set them aside.
In the bowl of a stand mixer add the brown sugar and slightly cooled butter. Beat on medium speed for about 2 minutes. Add egg and beat for one minute more. Add milk and vanilla extract and beat to incorporate.
Turn the mixer off, scrape down the sides of the bowl and add the dry ingredients all at once. With either the stand mixer on low, or by hand with a spatula, incorporate the dry ingredients until just mixed inches Fold in the chopped nuts and white chocolate chips.
Scoop two teaspoon sized balls onto a lined baking sheet. Bake for 9-11 minutes or until cookies are golden brown. Remove from oven and let rest of the baking sheet for 3 minutes before removing to a cooling rack.