Preheat oven to 400°F. Cream together shortening, sugar, egg, and vanilla extract.
Sift together flour, salt, and baking soda. Add mixture to wet ingredients and stir in Greek yogurt.
Flour a surface and roll out cookie dough. Use the top of a jar or a biscuit cutter to make round cookie shapes.
Bake 8 minutes. Transfer to a cooling rack immediately.
In a medium bowl mix powdered sugar, butter, milk, and coconut extract with a mixer until thoroughly combined. Beat on high until frosting is smooth and fluffy.
Spread frosting on cooled cookies. Pour shredded coconut into a small bowl. Press each cookie, frosting side down, into shredded coconut. Store in an airtight container. Makes 24 cookies.