Preheat oven to 350°F.
Combine butter and sugar in the bowl of a stand mixer.
Beat for 2 minutes on speed 2 using paddle attachment.
Add eggs, one at a time, and mix until combined.
Add yogurt and coconut extract, mixing on speed 4.
Scrape down the sides of the bowl, and mix again on speed 4 until batter is fully blended.
Add baking powder, salt and flour. Mix on low.
Form dough into balls the size of a walnut. Place on a parchment paper-lined baking sheet, leaving 2 inches between cookies.
Flatten balls of dough slightly.
Bake for 12 minutes. (They will not be golden.)
Transfer to a baking rack, and cool completely.
Make the frosting
Combine powdered sugar, coconut extract and 1 tablespoon milk; mix well.
Add extra milk, 1 teaspoon at a time, until desired consistency is reached.
Pour 1 cup of flaked coconut into a small bowl.
Frost cookies with glaze.
Dip frosted side of cookie in coconut, and return cookie to baking rack.
Add extra coconut to bowl, if needed.
Allow cookies to sit for 10 minutes for glaze to set.