Using a standmixer or a handmixer, cream together the butter and the granulated sugar until light and fluffy, about 2 minutes on medium-high speed, scraping down sides of the bowl as needed.
Reduce speed to low and beat in the egg, then the 2 tsp coconut extract.
In a small bowl, whisk together the flour, baking soda, salt, and baking powder.
With mixer on low, alternately beat in the flour mixture and the yogurt, scraping down sides of the bowl as needed, until all ingredients are just combined.
Use a standard ice cream scoop (2 ΒΌ-inch) to scoop out dough onto the prepared baking sheets. Place 5 scoops on one sheet, and place 5 scoops on the other. Leave plenty of room between scoops since the dough will spread in the oven.
Bake cookies at 350F for 10 minutes, then switch the baking sheets from top to bottom to ensure an even bake.
Bake for another 5 minutes, or until the cookies are lightly browned around the edges. Do not overbake!
Remove cookies from oven. Let cool on baking sheets for 5 minutes, then transfer to a wire rack to finish cooling. Cool cookies completely before icing them.
While cookies are cooling, mix together your two different icings (see below).