Preheat the oven to 350°F. Line a large baking sheet with parchment. Combine the flour, baking powder, salt, and sugar in a medium-size mixing bowl. Stir with a fork to combine.
Grate the cold butter and add the butter shreds to the flour mixture. Use a fork to mix the butter into the flour until it's evenly dispersed and approximately pea-sized.
Stir together 1/3 cup coconut cream, vanilla, and coconut extracts. Add the liquids and stir until a loose, dry dough forms. Add additional cream, only if needed. Gently fold in the coconut.
Use a medium scoop to portion 12-18 balls of dough onto a lined baking sheet. Press the cookies together with your hands, if the dough is crumbling. Bake for 18-20 minutes and remove from the oven when very barely browned on the bottom, taking care not to brown the tops of the cookies.
Transfer the cookies to a wire rack. While the cookies cool, combine the powdered sugar, milk, and coconut extract in a small bowl. Whisk until smooth. Add more cream or milk, just a few drops at a time, as needed to thin the glaze.
Drizzle the glaze over the cooled cookies and immediately sprinkle with coconut. Store in an airtight container. Enjoy!