Preheat oven to 375°F. Evenly spread coconut on a rimmed baking sheet. Bake in the oven until the coconut is toasted and the edges are well browned, 5 to 7 minutes. Remove to cool completely.

In a bowl, whisk together flour, salt, baking powder, and baking soda; set aside.

Using a stand mixer, cream together butter, granulated sugar, and brown sugar until lightened in color, about 3 minutes. Add milk, egg, and extracts. Beat until well incorporated and the volume has noticeably increased, about 3 minutes. Add dry ingredients and mix on low until just combined. Add coconut and stir to combine.

Line a rimmed baking sheet with parchment paper. Roughly scoop 2 tablespoons of cookie dough and shape into a ball. Place on cookie sheet and repeat shaping with remaining dough, placing each ball 1 1/2 inches apart from the others. Sprinkle each cookie with a little flake salt and bake until the edges are just golden brown, 14 to 15 minutes.