In the bowl of a food processor, combine flour, sugar, coconut, and salt (see note). Pulse until well blended.
Sprinkle butter cubes over top of the dry ingredients and pulse until dough begins to form a ball.
On a lightly floured surface, turn the dough out and knead gently into a smooth ball. Divide dough in half.
Place one dough half between two pieces of waxed paper. Roll dough out to about ¼" thick. Transfer dough to cookie sheet and refrigerate until dough is firm, at least one hour. Repeat with the second half of the dough.
Preheat oven to 325F and line two baking sheets with silpats or parchment paper.
Remove chilled dough from refrigerator and allow to warm on the counter until dough has softened slightly, about 10 minutes (the dough will shatter if you try to cut out the cookies while it's too cold).
Working with one half of the dough at a time, peel off the top sheet of waxed paper. Replace this sheet, turn the dough over, and remove the sheet that is now on top. Set top sheet of waxed paper aside.
Cut out desired shapes and place cookies on prepared baking sheets about ½" apart. Gather scraps and re-roll (replacing waxed paper sheet that was set aside earlier), chilling the dough as necessary. Repeat with second half of dough.
Bake cookies 10-12 minutes, rotating the baking sheets halfway through (see note). Cookies should be slightly firm and ivory in color. Cool on pan 5 minutes, then transfer the cookies to metal racks to cool completely.
Toasting Coconut:
Spread coconut out on *unlined* baking sheet. Toast coconut at 325F for approximately 5 minutes. Check on coconut and stir every minute or so to ensure even browning and avoid over-browning! Cool toasted coconut to room temperature.
Topping:
Place ⅔ of chocolate in a heatproof bowl over a small pan of simmering water. Make sure that the bowl doesn't touch the surface of the water.
Stirring often, warm chocolate until just smooth. Take bowl off the heat, and stir in remaining ⅓ of chopped chocolate. Stir until chocolate is smooth. This step will help to temper the chocolate, which will help the chocolate stay glossy after it sets.
Dip cookies in chocolate and top with toasted coconut however you desire. Enjoy!
Notes
Note on dried coconut: Be sure to use unsweetened, dried (desiccated) coconut. If you use the regular sweetened coconut that you find at the grocery store, the cookies will be REALLY sweet and you'll have a hard time keeping the cookie dough together and cutting out shapes because the pieces of coconut are so large. If you can't find unsweetened, dried coconut at your local grocery store, it's available [here].Note on use of food processor: My (small and old) food processor was barely able to do the job. It was full to the top, and I had to process the butter in batches. If you don't have a food processor or prefer not to use one, you can cut the butter into the dry ingredients by hand using a pastry cutter (like this one [here]) or a fork.Note on silpat/bake time: My cookies were about 2" x 2" and I baked on a silpat (like this one [here]). If you're making larger cookies, they may take an extra minute or two to brown. If your cookies are smaller and/or you aren't baking on a silpat, they will brown more quickly. Darker pans will also brown more quickly than lighter ones.Note on toasting coconut: Since you're using dried coconut, it will toast up (and burn!) faster than when you toast regular sweetened coconut. Make sure to keep an eye on it!