In a bowl, combine the butter, corn syrup, and granulated sugar using a stand mixer or handheld mixer until they're light and fluffy.

Add egg, vanilla and rum extract. Mix until well combined. Add flour, salt, baking powder, baking soda, cinnamon and nutmeg (if using). Mix until just combined. You should get a soft dough consistency.

Using a rolling pin, roll out the dough onto a piece of parchment paper to about 1/4″ thickness. 

Place the rolled out dough on a baking sheet then press another piece of parchment paper on top. Transfer the rolled out dough to the refrigerator for 1 hour (or 10 minutes in the freezer). Doing this will prevent the cookies from spreading while baking. Do not skip this step.

Preheat oven to 350 degrees F. Line a baking sheet with parchment paper. Set aside.

Remove the dough from the refrigerator. Using a round cookie cutter, make the cookie rounds. Transfer to the baking sheet. Re-roll the remaining dough and continue cutting until the entire dough is used. The cookies won't spread, so you can fit about 8-9 per baking sheet.

Bake for 11-14 minutes, depending on your oven. Remove from the oven and cool on a baking rack for 15 minutes before icing. The tops of the cookie should be smooth and the edges crispy and very lightly browned.

To make the coquito icing, mix together powdered sugar, coconut milk, rum extract and cinnamon in a bowl. The icing should be smooth and not too thick.

Dip each cookie into the icing, allowing excess to drip off, then place on a cooling rack. Sprinkle with shredded toasted coconut (see recipes notes). Allow the icing to set for 10 minutes before serving. Enjoy!