In a large mixing bowl, blend butter, sugar, and cooled cooked carrots together
Add Eggs One at a time until well incorporated, as well as vanilla extract
Sift flour, baking powder, and salt in a small bowl. Whisk in flaked/shredded coconut
Slowly mix dry ingredients with wet until a soft dough forms. Drop cookies 2" apart on lightly greased cookie sheet. A 1" cookie scoop works really well for this, or two teaspoons.
Bake at 400 degrees for 8-10 minutes.
Whisk frosting ingredients while cookies are baking, and promptly frost when cookies come out of the oven and are slightly warm.