Instructions

Process granulated sugar, brown sugar, and salt in food processor until no lumps remain, about 30 seconds. Add butter, egg yolk, and vanilla and process until smooth and creamy, about 20 seconds. Scrape down sides of bowl, add flour, and pulse until dough forms, 10 to 15 pulses. Transfer dough to counter and divide into 2 pieces, one twice as large as other. Roll small piece of dough into 4-inch log and wrap tightly in plastic wrap. Roll remaining dough into thicker 4-inch log and wrap tightly in plastic. Refrigerate logs until firm, at least 2 hours or up to 3 days.
Adjust oven racks to upper-middle and lower-middle positions and heat oven to 350 degrees. Line 2 baking sheets with parchment paper. Slice each log into ¼-inch-thick rounds. Place 1 large round and 1 small round with edges touching on prepared sheets. Repeat with remaining rounds, spacing them 1½ inches apart on sheets. Bake until edges are just golden, 17 to 20 minutes, switching and rotating sheets halfway through baking. Let cookies cool on sheets for 10 minutes, then transfer to wire rack and let cool completely.
Process coconut in food processor until finely chopped, about 10 seconds; transfer to bowl. Whisk confectioners' sugar and milk in separate bowl until smooth. Working with 1 cookie at a time, spread 1 teaspoon glaze evenly onto cookie, then sprinkle with coconut. Decorate with chocolate chips. Let glaze dry for at least 30 minutes before serving.