Place the oven racks in the middle and lower-middle positions. Preheat oven to 350 degrees F.
Line two baking sheets with parchment paper or silicone baking mats.
In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, ginger, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using electric hand beaters, add the butter and sugars and mix on medium speed until light and fluffy, about 1-2 minutes.
Add the eggs & vanilla and mix on medium speed until combined about 1 minute.
Dump in the dry ingredients and mix at a low speed until combined for about 30 seconds.
Fold in the carrots and shredded coconut.
Scoop 3 Tablespoons of the batter 2 inches apart on the prepared baking sheets. (I used a 3-Tablespoon scoop to make this a lot easier.)
Bake for 12 minutes, rotating the pans halfway through baking until the cake tops are just firm and spring back when pressed.
Let the cake tops sit on the pan for about 5 minutes, then transfer them to a wire rack to cool completely.
MAKE THE COCONUT CREAM CHEESE FROSTING:
In the bowl of a stand mixer fitted with the paddle attachment, or in a medium bowl using electric hand beaters, beat the cream cheese and butter on medium speed until smooth and no lumps remain for about 30-60 seconds.
Add the sifted powdered sugar, salt, and coconut extract and mix at medium speed until just combined, about 30-60 seconds.
TO FINISH:
Add about 2 tablespoons of the frosting to the flip side of one of the cake tops.
Top with another cake top to create your whoopie pie.
Roll the whoopie pies in toasted coconut.
Repeat to make 11 more whoopie pies.
Notes
Scrape down the sides of the bowl as needed in this recipe to ensure that everything is evenly combined.
Ensure that your eggs and butter are at room temperature. This will make them easier to mix into the batter and less likely to become over-mixed.
Use freshly grated carrots in this recipe, not the pre-shredded variety from the grocery store (the shred is too large for these whoopie pies).
If you don’t want lumpy frosting, ensure the cream cheese and butter are at room temperature.
Lastly, make sure you've sifted the powdered sugar.