Step 1Heat the oven to 300 degrees. Line several baking sheets with parchment paper and set aside.
Step 2Use a mixer to cream the butter, sugar, cinnamon and ginger. Add the syrup, rum and vanilla. Mix until smooth. Use a wooden spoon to stir in the cake flour, coconut and salt.
Step 3Use 1/2 teaspoon of batter for each cookie and drop onto the parchment paper, spacing 3 inches apart. Use your palm or the back of a spoon to slightly flatten.
Step 4Bake the cookies until lightly browned, about 17 minutes. Let rest 5 minutes. Use a metal spatula to transfer them onto paper towels to cool completely. Once cooled, store up to 5 days in an airtight container, at room temperature.
Step 5To serve, press a light sprinkling of powdered sugar through a fine sieve evenly over the surface of the cookies.
Step 6Variation: Make "cigarette-shaped" cookies by rolling them as soon as they come out of the oven. Bake only one sheet of cookies at a time. As soon as the sheet is out of the oven, use a small offset spatula to roll each warm cookie over the handle of a wooden spoon. If some cookies harden before you roll them, return them to the oven for several seconds until pliable.