Preheat oven to 350℉/175℃. Set rack in the center of the oven.
Line baking sheet with parchment paper. Set aside.
Sift together flour, baking powder and salt in a medium bowl. Set aside.
In a large mixing bowl (of stand mixer), with whisk attachment on high speed, beat the butter with the sugar until light colored. (3-4 minutes) (can also use hand held mixer).
Add egg and mix well. Make sure to scrape down the sides of the bowl.
Add yogurt, applesauce and vanilla. Combine thoroughly.
With mixer on low speed, add the flour mixture. Mix until just combined.
Gently combine carrots and coconut.
With a medium sized scooper, place dough on baking sheet.
Bake for approximately 12 minutes.
Cool on baking sheet for a couple of minutes before transferring to wire racks to cool.
Glaze if desired.
If desired cookies can be glazed. Whisk together 1/3 cup icing sugar with 1-1/2 - 2 teaspoons of orange juice. Glaze will be slightly runny. Can be adjusted to your own preference. If you desire more glaze per cookie, recipe can easily be doubled.Please keep in mind that the nutritional information provided below is just a rough estimate and variations can occur depending on the specific ingredients used. *recipe adapted from Worth Whisking