Cook 6 tablespoons butter in a small saucepan over medium heat until the butter turns golden brown color and takes on a nutty aroma (4 to 5 minutes). Take the saucepan off the heat and add remaining butter, stirring until melted. Set aside.
Add flour, milk powder, sea salt, baking powder and baking soda to a medium bowl, whisking to combine. Set aside.
Place butter and sugars in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium until loosely combined (30 seconds), then add eggs and vanilla and beat until combined (30 seconds). Add dry ingredients in 2 additions, beating until just combined. Scrape down the sides as needed. The dough will be a little wetter than a regular cookie dough given the higher fat content. Stir in chocolate chips and toasted coconut. Transfer cookie dough to the refrigerator and let chill for 30 minutes.
Preheat and oven to 375°F and set an oven rack to the middle position. Place 1 1/2-ounce slightly flattened rounds of cookie dough on a parchment-lined baking sheet about 1 inch apart. Sprinkle each with flaky sea salt. Bake for 12-14 minutes until the edges of the cookies start to brown. Let the cookies rest on the baking sheet for 5 minutes, then transfer to a rack to cool.