Combine coconut oil, sugar, and flaked coconut in the bowl of a food processor fitted with the blade attachment. Pulse a few times until coconut is ground and mixture feels like sand.

Add remaining ingredients and blend until mixture forms a ball, about 1 minute.

Divide dough into two pieces. Flatten into disks and roll each disk about 1/2-1/4 inch thick between two pieces of parchment paper. Place on a baking sheet and refrigerate for 20 minutes.

Heat oven to 375°F.

Cut dough into shapes and place an inch apart on parchment-lined baking sheet. Gather scraps and re-roll.

Bake 10-12 minutes or until dry in the middle. Let cool completely before frosting.

Combine all ingredients in the bowl of a stand mixer fitted with the whisk attachment. Whisk on low just until comes together then increase speed to high until smooth.